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Elements  of  Logic  ; 


DESIGNED    AS    A 


MANUAL    OF    INSTRUCTION 


BY 


HENRY    COPPfiE,    LL.D., 

PEESrDENT   OF  THE   LEHIGH    DNIVEESITT. 


REVISED    EDITlOy. 


NEW  YORK  • .  •  CI>XIXNATI  • .  •  CHICAGO 

AMERICAN    BOOK    COMPANY 


o' 


oS 


MmFim 


Entered  Mcotding  to  Act  of  Congress,  in  the  year  1867,  by 

E.  H.  BUTLER  &  CO., 

In  the  Clerk's  Office  of  the  District  Court  of  the  United  States  in  and  for  ths 
Eaatern  District  of  Pennsylvania. 


EnterM  according  to  Act  of  Congress,  in  the  year  15.2,  by 

E.  H.  BUTLER  &  CO., 
In  the  OflBce  of  the  tiibrarian  of  Congress,  at  Washington. 


E-P        1 


PREFACE 

TO    THE    REVISED    EDITION. 


In  obedience  to  the  public  demand,  the  publishers  have 
spared  no  expense  in  giving  to  this  volume  a  new  and 
more  attractive  form.     The  author  has,  on  his  part,  re- 
vised it  carefully,  and  added  much  important  matter,  some 
of  it  embodying  the  valuable  suggestions  of  instructors 
who  have  been  using  it  for  many  years.     Parts  of  the 
subject  have  received  fuller  illustration.     Parts  have,  after 
careful  deliberation,  been  omitted,  and  a  chapter  ha.s  been 
added  on  the  Fundamental   Laws  of  Thought  or  First 
Principles  of  Reason.     The  plan   and  divisions  of  the 
work  remain  the  same.     As  many  and  apparently  conflict- 
ing views  have  been  taken  of  the  meaning,  genus  and 
scope  of  Logic,  as  a  branch  of  Philosophy,  it  seems  proper 
to  say  that  much  of  the  diversity  is  nominal ;  that,  with 
differences  in  name,  most  treatises  admit  the  same  func- 
tions of  words,  conceptions,  propositions  and  arguments, 
and  that  the  chief  antagonism  arises  from  an  undue  exag- 
geration of  the  place  and  value  of  certain  functions  in  the 
reasoning  process.     This  remark  is  made  in  the  interest 
of  those  who  are  deterred  by  the  apparent  antagonism  of 
Bystenis  from  the  study  of  a  srience  most  of  the  detjiiU 


4  PREFACE   TO   THE    REVISED  EDITION. 

of  which  are  the  same  in  all  systems;  the  body  of  logical 
doctrines  recognized  by  all  logicians  do  not  refuse  to  com- 
bine harmoniously  in  one  system. 

In  the  present  edition  the  author  has  availed  himself 
of  the  voluminous  and  exhaustive  treatise  of  Sir  William 
Hamilton,  in  which,  together  with  the  expression  of  his 
peculiar  views  and  criticisms,  some  of  which  may  be  dis- 
sented from,  the  fiinctions  and  the  history  of  Logic  have 
been  set  forth  with  great  acuteness  and  erudition.  This 
has  led  the  author  to  slight  modifications  of  the  system 
of  Whately,  but  none  that  will  affect  the  general  import- 
ance and  soundness  of  his  views.  The  numerous  more 
recent  treatises  on  the  science  have  also  been  examined. 

It  is  confidently  hoped  by  the  author  and  the  pub- 
lishers that  the  favor  so  continuously  displayed  towards 
this  work  ever  since  its  appearance  fifteen  years  ago  will 
be  increased  by  its  additional  value  and  its  clear  and 
attractive  form ;  and  that  a  subject  frequently  regarded  as 
both  abstruse  and  vague  will  be  commended,  by  the  clear- 
ness and  simplicity  of  its  treatment,  to  many  who  have 
been  heretofore  doubtful  of  its  utility. 

H.  C. 

The  Lehigh  University,  August  1,  1872. 


PREFACE 

TO   THE   FIRST   EDITION 


The  following  treatise  has  been  written  in  the  ho])e 
that  it  may  supply,  in  some  degree,  a  real  want.  For 
several  years  the  author  was  a  teacher  of  Logic  in  the 
Military  Academy  at  West  Point,  where  the  subject  was 
thoroughly  studied  by  the  aid  of  Archbishop  Whately's 
text-book. 

How  much  a  manual  was  needed  before  that  work 
appeared  may  be  known  from  the  significant  fact  that, 
as  soon  as  it  was  published  as  an  article  in  the  Ency- 
clopaedia Metropolitana,  it  was  eagerly  caught  at  by  the 
community  of  teachers,  and  used,  unaltered,  as  a  book 
for  college  instruction,  on  both  sides  of  the  Atlantic. 

Since  the  publication  of  that  article  many  have  at- 
tempted the  preparation  of  a  manual  which  should  have 
the  instruction  of  classes  as  its  original  design  ;  but  the 
soundness  of  Whately's  views  and  the  conciseness  of  his 
expression  still  gave  to  his  work  the  greatest  circulation. 
Among  so  many  endeavors  the  author  would  venture 
to  express  the  hope  that  his  little  manual  may  find  its 
special  purpose  and  mission.  It  is  short ;  it  is  explana- 
tory of  all  the  difficult  points  so  often  left  to  confuse  a 
1*  6 


6  PREFACE   TO   THE    FIRST    EDITION. 

student ;  the  arrangement  is  simple,  and  much  that  in  a 
larger  treatise  would  be  of  necessity  included  is  here 
omitted,  so  that  what  the  student  learns  in  the  limited 
time  of  a  college  term  he  may  learn  well,  and  retain  in 
his  memory  as  a  basis  for  further  investigations.  To 
some  persons  it  may  seem  too  much  simplified ;  but  let 
it  be  remembered  that  it  is  a  manual  for  youth,  and 
that  its  only  aim  is  to  teach  them  the  Elements  of  Logic 
as  the  foundation  of  all  reasoning. 

The  basis  of  the  work  is  "  Whately's  Logic'' ;  many  of 
the  examples  are  taken  directly  from  that ;  so  many,  in- 
deed, that  the  acknowledgment  is  here  made  for  them  all, 
and  for  much  that  is  excellent  in  arrangement  and  in 
expression.  As  the  clear  expounder  of  Aristotle,  and  the 
originator  of  much  that  is  valuable,  Whately  must  stand 
at  the  head  of  the  Logicians  of  this  age.  The  author 
would  refer  specially  also  to  the  material  assistance  ob- 
tained from  ^^ Devey's  Logic''  (Bohn's  series);  "Aristotle's 
Post  and  Prior  Analytics"  (Bohn's  translation);  "Neil's 
Art  of  Reasoning;"  "Blakely's  Historical  Sketch  of  Logic;" 
"Lord  Bacon's  New  Organon;  Arnauld  (Logique  de  Port 
Royal) ;  /.  Bentham's  "Book  of  Fallacies."  From  Neil  a 
few  of  the  examples  have  been  taken. 

Besides  these,  he  has  consulted  a  great  number  of  works, 
the  aid  derived  from  which  is  so  general  that  they  do  not 
require  special  mention. 

University  of  Pennsylvania,  July,  1857. 


TABLE  OF  CONTENTS. 


CHAPTER  1. 

Logic,  the  Meaning  of  the  Term,  and  the  Scope  of  the 

Science. 

PAQI 

Section  1.  Of  the  term  Logic 13 

2.  Sources  of  Error 14 

3.  Logic  and  Philosophy 15 

4.  Logic  and  Rhetoric 17 

5.  Objection  to  Logic  as  an  Art 18 

6.  Natural  Logic 20 

7.  Systematic  forms  of  Error 21 

8.  Of  Method 22 

9.  Analysis  and  Synthesis 23 

10.  Analysis  and  Synthesis  as  applied  to  Logic 27 

1.  Analytical  View.     2.  Synthesis 27 

3.  Historical  View 28 

CHAPTER  II. 

Analytical  View  of  Logic. 

Section  11.  The  Reasoning  process  Analyzed 29 

The  Dictum  of  Aristotle 31 

CHAPTER  III. 
A  Synthesis  of  Logic. 

Section  12.  Of  certain  operations  and  states  of  the  Mind  used  in 

the  process  of  Argument 35 

7 


8  TABLE    OF    CONTENTS. 

PA«1 

1.  Apprehension 35 

2.  Judgment 36 

3.  Reasoning 37 


CHAPTER  IV 

Section  13.  Of  Terms 39 

14.  Division  of  Simple  Terms 10 

15.  Quantity  and  Quality  of  Terms 42 


CHAPTER  V. 
Op  those  Operations  which  Relate  to  Terms. 

Section  16.  Abstraction  and  Generalization 44 

17.  Species,  Genus  and  Differentia 45 

18.  Property  and  Accident 47 

19.  Of  the  different  orders  of  Genera  and  Species 48 

20.  Realism  and  Nominalism 5C 

21.  Definition  of  Terms 51 

22.  Nominal  and  Real  Definitions 53 

23.  Rules  for  Definition 54 

24.  Division 58 

25.  Recapitulation 62 


CHAPTER  VI. 

Sect'on  26.  Propositions 63 

27.  Simple  and  Compound 66 

28.  Quantity  and  Quality  of  Propositions 67 

29.  Of  the  Distribution  of  Terms  in  Propositions 70 

30.  Conversion .  - 73 

Illative  Converiion 76 

31.  Of  Opposition 78 

32.  Of  the  Matter  of  Propositions 79 

33.  Of  Compound  Propositions 81 

34.  The  Ne-y  Analytic 84 


TABLE    OF    CONTENTS.  & 

CHAPTER   VII. 

PASB 

Section  35.  Of  Arguments 87 

36.  Of  the  Syllogism 88 

37.  Logical  Axioms 89 

CHAPTER  VIII. 

Of  Figure  and  Moods. 

Section  38.  Figure 9c 

39.  Mood 98 

40.  Of  Reduction 107 

41.  Indirect  Reduction Ill 

42.  Notation  of  the  Syllogism 113 

CHAPTER  IX. 
Of  Irregular,  Informal  and  Compound  Arguments. 

Section  43.  Of  Abridged  Syllogisms 118 

44.  The  Sorites 121 

45.  The  Epichirema 124 

46.  Of  Hypothetical  Syllogisms 126 

Conditional 126 

DisjuDctive l-^O 

The  Dilemma 132 

CHAPTER  X. 

Fallacies. 

Section  47    The  Meaning  and  Comprehension  of  a  Fallacy 137 

48.  Fallacies  m  c/idione 138 

49.  Material  or  Informal  Fallacies 141 

Errors  in  the  Premisses 142 

Petitio  Principii 142 

Arguing  in  a  Circle 14- 

Non  causa  pro  causa 143 

Errors  in  the  conclusion 145 


10  TABLE   OF    CONTENTS. 

PAOl 

Irrelevant  conclusion 145 

Argumentum  ad  rem,  etc 148 

Changing  the  point  in  dispute 148 

Fallacy  of  Objections 149 

50.  Verbal  Fallacies 150 

1.  Etymology 152 

2.  Interrogations 153 

3.  Amphibolous  Sentences 154 

Causes  of  Ambiguity , 155 

51.  The  manner  of  removing  Ambiguity 160 

52.  The  Fallacy  of  Probabilities 161 

53.  Popular  Fallacies 163 


CHAPTER  XI. 

The  Fundamental  Laws  of  Thought  or  First  Principles 

OF  Reason. 

1.  Identity 167 

2.  Contradiction 168 

3.  Excluded  Middle 168 

4.  Reason  and  Consequent 168 


CHAPTER  XII. 

Section  54.  Of  certain  modes  in  which  Logic  is  applied 173 

Intuition,  Induction,  Deduction...., 173 

Argument  a  priori,  a  posteriori,  a  fortiori 176-178 

The  Investigation  and  Discovery  of  Truth 178 

1.  Observation • 179 

2.  Hypothesis 179 

3.  Induction 179 

4.  Theory 180 

Of  the  Nature  and  Kinds  of  Evidence 180 

Consciousness 180 

Sensation 180 

Analogy 181 

Induction 181 

Testimony 181 


I'ABLE    OF    (JONTENTS.  11 

CHAPTER   XIII. 

A  Historical  Sketch  of  Logic. 

PAOI 

•Section  55.  Division  of  the  Subject 182 

1.  Aristotle.  2.  Christianity  and  Logic.  3.  Bacon 
and  the  rise  of  Inductive  Science.  4.  The  Present 
System. 

56.  Aristotle 184 

The  Categories 188 

57.  The  Logic  of  Christianity 193 

58.  The  Logic  of  Experimental  Philosophy 200 

59.  Logic  in  the  18th  and  19th  centuries 209 

60.  Categories  and  Classification 211 

61.  Conclusion 217 

APPENDIX. 
Examples  FOH   Praxis 213 


LOGIC. 


CHAPTER  I. 

LOGIC:     THE  MEANING    OF  THE   TERM  AND    THE  SCOPE 
OF  THE  SCIENCE. 

(1.)  Of  the  Term  Logic. 

Logic  is  directly  from  the  Greek  XoytxTJ,  feminine  of  the 
adjective  Xoycxoq,  and  implies  i-iffr-qiirj  or  r^/viy — science  or  art. 
The  adjective  is  from  the  noun  logos.  As,  of  all  the  Greek 
words  which  have  been  transferred  to  our  English  speech, 
none  is  vaguer  and  more  subtle  in  its  meaning  than  the  word 
logos  (}'<>r>^),  so,  of  all  the  sciences,  none  has  been  less  clearly 
defined,  both  as  to  its  meaning  and  its  scope,  than  the  science 
of  Logic,  the  name  of  which  is  taken  from  that  word ;  and,  in 
consequence,  no  term  is  more  erroneously  applied  and  more 
frequently  misapplied  than  the  name  itself 

Ijogos  means  both  thought  and  speech,  and  the  earlier  writers 
distinguish  it  as  being  both  that  in  the  mind  and  that  without 
Combining  these,  logos  came  to  mean  discourse,  and  hence 
some  writers  have  supposed  Logic  to  be  simply  the  science  of 
spoken  or  written  language,  thus  confounding  it,  in  part,  with 
Rhetoric,  and  even  with  Grammar;  others,  considering  dis- 
:ourst  to  imply  not  simply  the  written  symbol  or  the  spoken 
smmd,  but  also  the  expression  of  the  thought,  have  more  cor- 
rectly supposed  Logic  to  be  the  Science  of  the  Laws  of  Thought, 
and,  as  such,  a  branch  of  metaphysics,  or  the  science  whicli 
investigates  the  workings  of  the  mind ;  others  still,  and  by  far 


14  LOGIC. 

the  greater  number,  regarding  it  as  a  union  of  language  and 
thought  in  the  deduction  of  truth,  have  claimed  that  it  had 
to  do  with  the  subject-matter  of  scientific  investigation,  and 
have  thus  erred  more  widely  than  all  by  confounding  Logic 
with  the  labors  of  physical,  metaphysical  and  ethical  philoso- 
phy rather  than  an  instrument  for  the  service  of  them  all,  as 
it  really  is. 

It  seems  necessary,  then,  at  the  beginning  of  a  treatise  on 
this  subject,  to  define  the  meaning  of  the  word,  and  the  true 
scope  of  the  science,  before  we  undertake  its  study — to  rid 
ourselves,  as  it  were,  of  the  mists  which  surround  us,  before 
we  can  even  see  clearly  the  field  in  which  we  are  to  labor. 

(2.)  Sources  of  Error. 

Many  accurate  thinkers  have  confused  the  minds  of  stu- 
dents by  producing  books  which,  while  they  contain  a  just 
view  of  the  logical  system  itself,  attempt  at  every  step,  as  has 
been  said,  to  explain  the  subject-matter  upon  which  this  system 
is  employed,  and  which  forms  no  part  of  it;  while  many 
others,  adopting  strongly  the  views  of  those  who  have  initiated 
so-called  systems  of  logic,  have,  as  partisans,  carried  forward 
from  period  to  period  old  errors  and  old  perplexities ;  and, 
themselves  ignorant  of  the  subtleties  which  surround  them, 
have  called  their  views  the  true  logic,  and  those  of  every  other 
writer  false.  Others  again  have  endeavored,  in  an  amiable 
but  unscientific  spirit,  to  harmonize  all  the  schemes  of  the 
philosophers,  and  to  call  the  result,  full  of  error  and  inexact- 
ness, the  system  of  Logic. 

There  are,  indeed,  in  the  systems  of  the  great  philosophers 
many  parts  that  are  mutually  dependent,  and  true  science 
will  be  found  to  harmonize  with  itself  everywhere.  But  since 
there  is  also  error  in  them  all,  no  mere  greatness  of  name 
should  exempt  from  the  scrutiny  and  exposure  of  error. 

We  must  take  care  to  distinguish  between  the  difiPerent 
functions  of  the  intellect,  so  as  to  call  things  by  their  right 


LOGIC   AND    PHILOSOPHY.  15 

names — not  including  in  the  name  Logic  what  belongs  to 
Physics  or  Metaphysics,  but  laying  down  at  the  outset  the 
limits  and  province  of  that  system  which  we  wish  to  designate 
by  the  word  Logic.  If  we  can  do  this  we  shall  have  accom- 
,  plished  very  much  at  the  beginning,  and  shall  find  our  labor 
easy  as  we  proceed. 

If  we  would  see  how  important  it  is  rightly  to  understand 
this  fact  of  the  ambiguity  of  the  word  Logic,  as  frequently 
employed,  we  need  but  look  for  a  moment  at  the  errors  into 
which  modern  philosophers  have  fallen  when  speaking  of  the 
Logic  of  Aristotle  as  compared  with  the  Logic  of  Bacon. 
This  has  been  fostered  by  the  fact  that  while  Aristotle  set 
forth  his  logical  views  in  his  Organon,  Bacon  produced  a 
Novum  organum  or  new  organon.  If,  as  we  shall  endeavor  to 
demonstrate.  Logic  is  the  science  which  controls  the  universal 
and  ultimate  principle  of  reasoning,  given  to  man,  just  as 
speech  was  given  to  him,  by  a  beneficent  Creator,  then  it  is 
not  Aristotle's  Logic,  nor  Bacon's  Logic,  but  a  single  universal 
Logic,  given  to  man  as  the  rule  of  his  reason,  which  must  be 
intelligible  and  harmonious  wherever  and  by  whomever  it  is 
used. 

(3.)  Lo^c  and  Philosophy. 

In  this  consideration  another  word  plays  a  prominent  part. 
The  word  which  has  been  pressed  into  service,  to  denote  the 
peculiar  progress  of  great  minds  in  the  domains  of  Truth,  is 
''Philosophy ;"  but  even  the  word  "Philosopher,"  said  to  be 
adopted  by  a  wise  ancient*  as  a  more  modest  title  than  ffoipo:;, 
as  the  sages  of  Greece  were  called,  has  been  productive  of 
great  confusion.  "Philosophy"  has  been  made  to  stand  for 
a  thousand  sciences,  and  to  preside  in  the  kingdoms  of  mind, 
morals,  and  physics,  until  to  be  a  philosopher  means  to  pursue 
one  of  many  intellectual  pursuits,  and  Philosophy  unqualified 
means  everything  or  nothing. 

*  Pythagora-s. 


16  LOGIC. 

And  yet  this  vague  and  inexact  term  Philosophy  \^ 
the  one  which  has  been  most  frequently  confounded  with 
Logic,  and  a  want  of  clear  definition  and  of  a  just  under- 
standing in  the  dispute  has  led  to  the  production  of  in- 
exact, distorted,  and  conflicting  systems,  both  of  Philosophy 
and  Logic,  which  have  confused  those  desirous  of  learning, 
and  deterred  many  from  the  difficult  and  perilous  attempt. 
In  attempting  to  reach  a  clear  division  and  definition  of 
Philosophy  and  Logic,  the  followers  of  Plato  asserted 
Logic  to  be  a  part — and  the  instrument — of  Philosophy. 
The  Stoics  divided  Philosophy  into  three  parts,  viz. : 
Physics  or  Theoretical  philosophy ;  Ethics  or  Practical 
philosophy,  and  Login,  a  subsidiary  part,  instrumental  to 
the  others. 

Indeed  both  words,  and  the  errors  to  which  their  use  has 
led,  indicate,  at  once,  the  yearning  and  the  weakness  of  the 
human  mind — the  desire  of  man  to  investigate  and  systema- 
tize truth,  combined  with  the  obscurity  and  doubt  which 
beset  his  investigations  at  every  step. 

The  acuteness  of  the  Greeks,  upon  which  had  been  grafted 
all  the  power  and  attainment  of  the  Oriental  world,  could 
reach  no  clearer  nomenclature  than  to  call  their  studies  and 
their  inductions  Philosophy — the  love  rather  than  the  attain- 
ment of  wisdom — and  the  art  by  which  they  reasoned  from 
truth  to  truth,  by  which  they  progressed  from  parallel  to  par- 
allel in  the  sea  of  doubt  and  uncertainty,  Logic,  the  art  of 
words  or  discourse,  the  very  mention  of  which  suggests  a 
dubious  question,  and  calls  up,  as  it  were,  two  opponents  in 
considering  it. 

Without  considering  the  numerous  definitions,  we  may 
agree  to  call  Philosophy  a  search  for  final  causes,  in  accord- 
ance with  a  primary  law  of  the  mind,  which  demands  a  cause 
for  everything,  and  also  in  obedience  to  the  tendency  of  all 
science  to  unity.  This  covers  the  investigation  cf  truth  as 
ko  its  subject  matter:    the  processes  of  collating  and  com- 


LOGIC    AND    RHETORIC.  17 

paring  material,  and  of  classifying  and  aggregating  observa 
tious  and  experiments. 

Logic  we  shall  consider  the  science  which  guides  the  ope- 
ration of  thought  from  simple  intuitions  and  conceptions, 
through  judgments,  to  the  simple  reasoning  process,  by  which 
we  pass  from  truth  to  truth  already  found,  and  by  which  we 
guard  against  fallacious  arguments  in  the  passage. 

(4.)  Logic  and  Rhetoric. 

The  exact  line  between  Logic  and  Rhetoric  is  not  always 
clearly  drawn.  The  distinction  between  them  may  be  thus 
stated :  Rhetoric  is  the  art  of  inventing,  arranging  and  ex- 
pressing thought  in  discourse,  or,  in  brief,  it  is  the  Art  of  Dis- 
course. Rhetoric  finds  terms,  propositions  and  arguments  in 
the  construction  of  discourse,  and  arranges  and  clothes  them 
with  language  to  produce  a  certain  effect. 

It  is  the  province  of  Logic  to  test  the  Rhetorical  operations, 
and  particularly  to  declare  of  its  arguments  whether  they  are 
valid  or  invalid.  Thus,  in  its  relation  to  Rhetoric,  Logic  is  a 
check  and  an  ordeal ;  an  arbiter  of  the  reason  ;  a  detecter  of 
what  is  false  and  fallacious. 

In  this  view  Rhetoric  includes  Grammar.  Thus  a  dis- 
course may  be  grammatically  correct,  and  rhetorically  ele- 
gant, and  yet  full  of  error  as  to  its  Logic. 

Having  thus  seen  that  the  name  Logic  is  in  a  great  degree 
arbitrary,  and  that  we  should  not  attain  to  an  understanding 
of  the  subject,  if  we  followed,  even  remotely,  the  etymology 
of  the  word,  we  repeat  that  Logic  has  to  do  neither  with  the 
words  themselves — except  as  they  are  arranged  into  terms, 
propositions  and  arguments — nor  with  their  meanings,  except 
as  related  to  reasoning,  i.  e.,  passing  from  two  known  and  ao- 
knoivledged  judgments  to  a  third,  which  is  derived  from  their  com- 
bination. With  this  explanation,  then,  we  may  state  the  defi- 
nition of  the  term.  Logic  is  the  Science  and  the  Art  of  Rect- 
trniing ;  and  reasoning  is  the  ultimate  process  of  thought  in 
J*  B 


18  LOGIC. 

its  search  for  the  True,  the  end  proposed  to  us  by  our  cogni 
tive  faculties. 

Of  these  two  terms,  Science  and  Art,  we  remark  that  Art  ia 
in  a  critical  sense  more  extensive  than  Science,  since  the  ^prao- 
tice  of  an  Art  implies  the  application  of  the  principles  of 
Science,  while,  on  the  other  hand,  Science  might,  indeed  does, 
exist  in  its  theoretic  state  without  being  put  to  practical  use. 
The  Science  would  be  the  investigation  of  the  principles  upon 
which  the  human  mind  is  based  in  reasoning,  and  the  Art  the 
application  of  those  principles  to  the  establishment  of  prac- 
tical rules  for  conducting  the  process.  Logic  may  then  be 
more  simply  defined  the  Art  of  Reasoning,  and  as  such  we 
shall  consider  it  in  these  pages,  less  concerned  about  the 
composition  of  man's  reason  than  about  the  practical  laws 
and  methods  by  which  it  works. 

Before  proceeding  to  explain  the  system  of  Logic,  which 
has  developed  itself  sinc6  the  days  of  Aristotle,  let  us  meet 
at  the  threshold  some  plausible  objections  which  have  been 
brought  against  the  establishment  of  any  system  whatever. . 

(6.)  Objection  to  Logic  as  an  Art. 

As  man  has  been  universally  gifted  with  reason,  by  means 
of  which  he  may  combine  his  thoughts  and  arrive  at  just 
conclusions,  and  with  language  in  which  to  communicate 
them,  it  is  asserted  that  every  man  carries  his  own  Logic 
within  him,  as  the  immediate  gift  of  God. 

All  men  reason,  it  is  true,  and  many  men  are  not  aware  of 
the  logical  process  which  they  use ;  and  this  has  been  made, 
even  by  men  of  acute  minds,  an  objection  against  Logic ;  for, 
they  say,  since  men  reason,  and  reason  well,  without  rules, 
and  without  knowing  the  process,  a  system  of  rules  must  be 
unnecessary. 

The  objection  is  plausible,  and  has  been  fruitful  of  evil. 
But  as  it  is  one  which  may  be  brought  against  many  other 
arts  as  well  as  Logic,  it  may,  we  think,  be  most  easily  met 


OBJECTION    TO    LOGIC    AS    AN    ART.  U* 

and  most  clearly  refuted  by  illustration.  Many  children 
speak  with  correctness  and  precision  before  they  have  an} 
knowledge  of  Grammar ;  and  there  are  persons  of  wonderful 
powers  in  arithmetical  computation  who  have  never  learned 
Arithmetic;  but  Grammar  and  Arithmetic  are  not  for  such 
reasons  condemned  :  their  rules  are  an  infallible  test  for  pre- 
cise speaking  and  correct  computation,  and  are  thus  guides  to 
the  weaker  and  slower  intellects— and  these  constitute  the 
immense  majority  of  mankind — to  keep  them  from  formal 
error.  So,  too,  in  Music  and  Painting ;  great  geniuses  arise 
in  both  Arts,  but  no  one  would  contend  that  hard  study,  ac- 
cording to  the  established  systems  of  the  great  composers  and 
the  great  masters — established  upon  the  true  principle  of 
voice  and  ear  and  eye — is  not  absolutely  requisite  to  excel- 
lence and  success. 

Many  persons  of  clear  perceptive  faculties,  and  who  form 
and  combine  their  judgments  rapidly,  may  reason  acutely 
and  well  without  a  system  of  rules  ;  but,  in  order  to  be  certain 
of  their  correctness,  others  must  have  some  invariable  test ; 
on  the  other  hand  there  are  many,  of  quick  but  erratic  minds, 
who  reason  with  such  dangerous  sophistry  that  the  most  deli- 
cate logical  tests  alone  can  expose  the  fallacy,  of  which  in- 
deed they  may  not  themselves  be  entirely  aware.  As  such 
delicate  tests  have  not  been  within  the  reach  of  the  multi- 
tude, it  is  thus  that  men  have  become,  for  want  of  a  popular 
knowledge  of  Logic,  at  once  self-deceivers  and  deluders 
of  mankind:  have  established  illogical  religious  creeds, 
monstrous  social  fallacies,  false  theories  of  government,  which 
are  immediately  made  manifest  by  the  simple  application  of 
Logic. 

Nay,  more :  since  Logic  is  the  science  which  develops  the 
one  universal  principle  of  Reasoning,  applied  alike  to  every 
branch  of  science,  Exact  or  Inductive,  it  seems  much  more 
necessary  that  we  should  establish  full  and  unerring  rules  for 
our  guidance,  and  thus  be  kept,  at  every  turn,  from  the  mani- 


20  LOGIC. 

fold  errors  which  arise  from  systems  based  upon  such  objec- 
tions as  those  we  have  mentioned. 

(6.)  Natural  Logic. 

The  natural  laws  which  govern  the  human  mind  in  ita 
attempts  to  reason  have  been  called  by  the  opposers  of  Logi- 
cal systems  Natural  Logic.  We  accept  the  name,  and  are 
ready  to  allow  that,  in  following  these  laws,  reason  is  right, 
and  originally  perfect  in  applying  them  ;  but  now,  in  the  fallen 
condition  of  man,  reason  is  certainly  liable  to  be  biased  by 
prejudice,  distorted  by  passion,  or  insidiously  tempted  into 
open  error.  Thus  many  men,  who  reason  correctly  on  most 
subjects,  are  swayed,  in  one  or  more,  by  self-interest,  partisan- 
ship, fashion,  predominance  of  the  imagination,  and  such  like 
causes ;  and  thus  men  of  equally  clear  minds  in  the  main, 
from  the  same  premises  draw  different  conclusions,  or  estab- 
lish the  same  conclusion  by  very  different  premises.  Thus 
also  the  same  man,  at  different  periods  of  his  life,  or  swayed 
by  various  circumstances,  will  reason  differently ;  and  from 
such  causes,  it  is  evident  that  each  man's  natural  Logic  is  not 
a  sufficient  guide  for  his  reason.  Besides,  reason  does  not 
confine  itself  to  the  immediate  conclusion  flowing  from  these 
fundamental  laws  of  reasoning,  but  is  constantly  drawing  one 
conclusion  from  another.  Now,  in  this  process,  reason  cer- 
tainly needs  more  than  these  natural  laws  to  keep  it  from 
error. 

Yet  still  it  is  from  this  natural  Logic,  or,  rather,  the  con- 
currence of  the  right  reason  of  many  well-ordered  minds,  that 
the  science  of  Logic  has  been  deduced. 

By  a  systematic  observation  of  such  minds,  as  they  reason, 
taking  care  to  remove  all  causes  of  error  in  each  particular 
case,  we  establish  rules  for  the  reason,  and  are  able  to  detect, 
by  the  application  of  these  rules  to  other  cases,  every  falla- 
cious argument  resulting  from  such  causes  of  error. 

There  must  have  been  reason  before  there  (;ould  be  a  sys- 


8Y8TEMATI('    FORMS    OF    ERROR.  21 

tem  of  laws  to  govern  it,  just  as  we  know  there  was  language 
before  Grammar  was  formed.  It  was  to  systematize  this 
reason,  to  methodize  this  natural  Logic,  and  particularly  to 
guard  against  errors  in  the  use  of  the  reasoning  powers,  that 
a  canon  was  prepared,  and  that  a  complete  science  of  Logic 
hai?  been  formed. 

We  have  spoken  in  general  terms  of  the  confusion  and 
error  which  have  grow^n  out  of  the  misapprehension  of  Logic. 
The  more  special  phases  of  it  are  those  resulting  from  an 
attempt  to  systematize  these  general  erroneous  notions. 

(7.)  Systematic  Forms  of  Error. 

By  a  very  common  misuse  of  language,  we  hear  such 
phrases  as  " math&)natical  reasoning,''  " moral  reasoning,''  "syl- 
logistic reasoning,"  and  "inductive  reasoning;"  which  would 
lead  us  to  suppose  that  instead  of  one  there  were  many  kinds 
of  reasoning.     This  is  a  fruitful  source  of  error. 

These  so-called  different  kinds  of  reasoning  are  only  appli- 
cations of  Logic  to  different  subjects  and  different  habits  of 
thought.  The  Logic  in  each  is  the  same  ;  the  subject-matter 
alone  is  different. 

It  would  seem  unnecessary  to  dwell  upon  this  point,  but  it 
has  been  so  commonly  misunderstood,  and  the  error  has  been 
so  disseminated  by  professional  writers  upon  Logic,  that  it 
must  be  plainly  stated  and  carefully  remembered. 

When  we  speak,  then,  of  a  good  mathematician,  we  mean 
one  who  is  able,  most  surely  and  rapidly,  to  apply  Logic  to  the 
investigations  of  numbers  and  quantity.  When  we  hear  of  a 
great  theologian,  we  know  that  he  has  amassed  much  theo- 
logical learning,  and  has  applied  Logic  to  it  successfully.  So, 
too,  with  other  sciences.  * 

In  general,  in  whichever  of  the  myriad  fields  of  nature 
and  mind  ardent  votaries  may  wander,  however  various  the 
stores  they  may  amass,  they  must  all  come  back  with  their 
sheaves  to  the  great  measuring-centre  of  Logic,  and  apply 


22  LOGIC. 

its   dicta    before  they  can   compute   or   use  their   gathered 
gains. 

The  value  of  Logic  as  a  study  is  manifold.  Not  only  is  it 
an  infallible  test  of  argument,  but  it  strengthens  and  disci- 
plines the  mind,  giving  it  system  and  method ;  and  it  has 
established  a  terminology  of  universal  adoption  and  applica- 
ble to  all  its  practical  adaptations  in  science.  Thus  it  gives 
uniformity  to  the  investigation  of  all  branches  of  science. 

(8.)  Of  Method. 

Method  is  the  order  and  arrangement  of  facts  to  produce  a 
certain  result ;  to  establish  new  truth,  to  investigate  old,  and 
to  explain  and  teach  both.  It  is  derived  from  the  Greek 
fieff'odou,  which  denotes  the  way  through  which  we  arrive  at 
a  certain  result.  Method  is  employed  in  every  science,  and 
plays  a  specially  important  part  in  Logic. 

Whatever  steps  are  taken  to  make  knowledge  profitable,  to 
reduce  theory  to  practice,  and  to  give  clear,  distinct  and  con- 
nected ideas  of  science,  constitute  Method.  The  extension  of 
the  term  Method,  it  is  evident,  will  differ  according  to  the 
subject  to  which  it  is  applied. 

The  methods  of  investigation  differ  slightly  for  the  different 
kinds  of  science,  but  may  generally  be  classified  under  two 
heads.  Analysis  and  Synthesis,  of  which  the  former  is  generally 
used  in  the  private  investigation  of  truth,  and  the  latter  for 
the  purposes  of  instruction. 

The  successive  stages  in  the  discovery,  progress  and  estab- 
lishment of  any  science  are  three,  viz. :  the  descriptive,  the 
inductive  (also  called  the  experimental),  and  the  deductive  or 
exact  stage. 

As  soon  as,  by  the  description  of  a  science,  the  statement 
of  its  present  condition,  its  wants,  its  unknown  causes,  etc.,  we 
have  a  just  representation  of  it,  we  proceed  to  observation 
and  experiment,  or  induction;  and  when,  by  iyiduction,  or  the 
labored  collection  of  many  particular  facts  and  examples,  we 


ANALYSIS   AND   SYNTHESIS.  23 

have  established  general  laws,  we  may  then  deduce  from  them 
any  particular  fact  or  facts  which  it  concerns  us  to  know. 

These  stages  of  investigation  belong  equally  to  the  physical 
and  moral  sciences,  with  the  slight  difference  in  practice 
that  the  vagueness  and  complexity  involved  in  mental,  spirit- 
ual and  social  phenomena,  which  all  belong  to  the  moral 
sciences,  require  more  delicate  and  subtle  agencies  to  trace 
their  laws  than  those  of  the  natural  world  around  us. 

And  the  sources  of  experiment  are  not  at  all  analogous. 
Here  we  are  surrounded  by  apparent  contradictions.  The 
world  of  nature  is  changeable  and  shifting,  and  yet  it  is  pal- 
pable to  our  senses ;  the  laws  which  govern  it  are  mysterious 
and  inscrutable,  and  yet  thjey  are  constant ;  the  moral  world, 
which  is  unchangeable  and  eternal,  is,  when  considered  or 
examined  by  unaided  reason,  vague  and  obscure,  and  the 
abstract  conclusions  to  which  our  inductions  lead  us,  positive 
and  incontrovertible  as  they  are,  are  but  few  and  unsatis- 
factory. 

We  shall  have  occasion  to  consider  the  subject  of  Method 
more  in  detail  hereafter,  but  at  present  we  design  to  apply  it 
to  the  consideration  of  Logic. 

We  speak  of  the  method  of  a  single  science,  or  a  Method 
which  is  applied  to  all — as  in  that  which  leads  to  the  Classifi- 
cation of  the  sciences.  In  either  investigation  the  division 
of  Method  into  Analysis  and  Synthesis  is  a  just  one,  as  both 
are  used  in  either  process. 

(0.)  Analysis  and  Synthesis. 

To  illustrate  more  clearly  the  nature  of  these  two  processes, 
let  us  take  a  familiar  example.  If  we  designed  to  teach  a 
person  how  to  make  and  use  some  complicated  structure,  as, 
for  example,  a  ship,  and  if  this  person  had  never  seen  one, 
the  first  step  in  the  process  would  be  to  show  him  the  ship 
completely  built  and  ready  to  proceed  to  sea,  fully  rigged, 
equipped  and  manned,  that  he  might  take  in  at  a  glance  its 


24  LOGIC. 

finished  appearance,  and  its  ultimate  design  and  use:  in  a 
word,  that  he  might  know  what  he  was  to  learn  to  make. 
This  would  be  the  first  lesson  in  ship-building.  The  next 
Btep  would  be  to  show  it  to  him  partially  dismantled,  or,  in 
effect,  to  take  it  to  pieces  before  his  eyes,  that  he  might  see 
the  parts  of  which  it  is  composed,  and  their  relative  position 
in  the  structure. 

The  third  step  would  be  to  show  him  how  each  part  was 
made,  and  to  let  him  see  them  all  in  minute  detail  lying 
together,  according  to  some  system,  which  should  be  prepara- 
tory to  a  reconstruction  of  the  ship. 

This  process  of  successive  steps  is  Analysis,^  or  a  dissolu- 
tion of  anything  into  its  elements. 

In  the  investigation  of  any  science,  it  is  of  primary  import- 
ance. Showing  us  at  first  the  scope  and  design  of  the  science, 
by  systematic  degrees  it  decomposes  it  into  its  elements,  and 
prepares  us  for  intelligent  study  of  its  many  forms. 

This  operation  shows  us  also  the  simplicity  of  science,  and 
is  evidently  derived  from  the  teachings  of  nature ;  for,  while 
there  are  innumerable  forms  of  animal  and  vegetable  life,  the 
analysis  of  nature  which  is  constantly  going  on  shows  but 
few  parts  or  elements  in  all  her  works,  and  great  simplicity 
of  combination  of  the  same  elements  in  different  proportions, 
to  produce  the  most  dissimilar  forms  and  results.  So  all 
the  sciences,  physical,  intellectual,  and  moral,  while  they 
assume  many  and  varying  forms,  are  in  reality  composed  of 
a  few  simple  elements  of  nature  or  mind,  and  this  their 
analysis  displays. 

The  analysis  of  physical  science  is  of  course  the  most  exact 
of  these  processes,  in  proportion  as  the  things  of  sense  are 
easier  to  comprehend  and  fix  than  those  of  mind  and  spirit ; 
in  physics,  this  process  of  analysis  is  carried  from  the  grandest 
class,  such  as  kingdoms  and  high  genera,  to  the  observation 
and  use  of  atoms  and  molecules  inconceivably  small,  which 
^  avaAvu — to  separate  into  elements. 


ANALYSIS    AND    SYNTHESIS.  25 

are  to  constitute  the  basis-elements  of  a  reconstructing  pro- 
cess. Accurate  analysis  is  a  work  of  patient  labor.  Chance 
experiments  have  indeed  occasionally  produced  great  results, 
but  this  is  an  argument  for,  rather  than  against,  careful 
analysis.  Roger  Bacon  discovered  a  fulminating  powder 
when  he  was  not  seeking  it ;  but,  to  be  useful,  this  powder 
roust  cease  to  be  a  chance  discovery ;  that  is,  it  must  be  anar 
lyzed  into  nitre,  charcoal,  and  hrbmtone,  so  that,  these  con- 
stituents once  known,  we  can  make  our  fulminating  powder 
at  will.  Science  has  never  proceeded  upon  chance ;  it  moves 
safely  only  when  it  moves  by  invariable  but  ever-extending 

laws. 

Incomplete  analysis  has  done  more  to  establish  and  per- 
petuate error  than  even  blind  superstition.  For  it  was  in 
the  face  of  the  latter  that  Copernicus  and  Galileo  established 
the  true  theory  of  the  heliocentric  system  ;  while,  before  their 
time,  the  incomplete,  false,  and  arbitrary  analysis  of  astron- 
omy, and  the  belief  in  stellar  influences,  which  a  just  anal- 
ysis would  have  destroyed,  led  all  the  writers,  from  the  time 
of  Ptolemy,  to  build  a  false  system  of  celestial  mechanics, 
and  thus  to  clog  the  wheels  of  true  science. 

The  process  of  analysis  having  been  completed,  we  come 
naturally  to  Synthesis."^ 

Having  taken  to  pieces,  we  proceed  to  the  other  task  of 
rebuilding :  carefully  examining  each  different  element  as 
they  all  lie  before  us,  until  we  understand  thoroughly  the 
material  of  which  it  is  made  and  its  construction,  we  proceed 
tc  adjust  it  to  its  place  in  the  structure ;  piece  by  piece,  per- 
b^ps  slowly  and  painfully,  we  build  the  ship,  until,  at  length 
it  is  complete ;  nor  is  the  labor  yet  finished :  we  launch  it 
upoi  the  waters,  spread  its  sails  to  the  wind,  and  see  it  in 
practical  and  successful  movement,  and  then  we  may  account 
oui-selves  acquainted  with  the  structure,  and  able  to  build  its 
like  whenever  called  upon  to  do  so. 

*  awTiBrinL — to  place  together. 

t 


26  LOGIC. 

This  operation  is  called  Synthesis ;  it  is  evident  that  it  is 
also  continually  going  on  in  nature  in  the  reproduction  oui 
of  crude  materials  of  the  many  forms  of  complicated  existence. 

Many  writers,  in  investigating  a  science,  begin  with  this 
latter  process,  entirely  neglecting  the  former ;  but  it  is  so 
evident  that  the  analysis  of  a  science  gives  large  and  valuable 
lessons  preparatory  to  its  synthesis,  or  real  study  for  ourselves, 
that  most  modern  treatises  on  science  have  adopted  and  fol- 
lowed this  order  of  instruction.  It  may  then  be  safely  stated 
that  in  any  science  the  true  synthesis  can  only  be  proportional 
to  a  vigorous  and  just  analysis,  and  there  have  consequently 
been  rules  laid  down  for  proceeding  to  consider  any  science 
or  art  in  pursuance  of  this  method. 

The  rules  for  Analysis  may  be  reduced  to  these : 

1st.  Not  to  believe  any  general  scientific  statement  without 
proof;  that  proof  determined  by  the  just  principles  of  evi- 
dence. 

2d.  To  divide  every  scientific  dictum  into  as  many  parts  or 
elements  as  shall  be  necessary  to  resolve  it. 

3d.  To  make  a  methodical  arrangement  of  these  elements 
in  order  that  we  may  understand  them  clearly  and  the  rela- 
tion which  they  bear  to  each  other. 

Having  done  this,  the  corresponding  rules  for  Synthesis 
are: 

1st.  To  use  such  tevTns  to  express  the  elementary  parts  as 
are  free  from  ambiguity. 

2d.  In  combining  these,  to  assume  only  such  clear  princi- 
ples or  axioms  as  cannot  be  contested  by  any  persons. 

3d.  Ta  prove,  by  demonstration,  all  the  conclusions  at 
which  we  arrive,  in  the  employment  of  the  terms  and  axioms 
used. 

These  remarks  upon  analysis  and  synthesis,  as  the  two  vital 
functions  of  Method  in  investigation,  and  as  the  two  necessary 
instruments  of  all  scientific  study,  are  designed  for  general 
application.     A  proper  and  constant  application  of  the  rules 


ANALYSIS  AND  SYNTHESIS  AS  APPLIED  TO  LOGIC.       27 

of  analysis  and  synthesis  would  cause  great  advancement  in 
our  studies,  and  would  go  far  to  insure  us  from  error,  however 
rapid  that  advancement  might  be.  Analysis  and  synthesis 
are  conducted  by  means  of  abstraction,  generalization,  defin- 
ition and  division,  which  will  be  referred  to  hereafter.  We 
have  placed  the  subject  of  Method  in  this  place,  because  we 
design  to  use  it  in  application  to  the  study  of  Logic  itself;  for, 
as  a  science  to  be  studied.  Logic  comes  under  the  rules  which 
have  been  just  laid  down. 

(10.)  Analysis  and  Synthesis  as  applied  to  Logic. 

Now,  let  us  employ  this  method  in  investigating  the  science 
of  Logic. 

Abstract  or  formal  logic  is  an  explication  of  the  laws  of 
thought  and  the  rules  of  reasoning,  without  regard  to  any 
subject-matter.  Applied  logic  is  the  application  of  these  rules 
to  the  subject-matter  of  scientific  investigation.  It  is  only 
with  the  first  of  these  that  we  at  present  have  to  do. 

That  we  may  study  the  subject  profitably,  making  each 
step  a  preliminary  to  the  due  understanding  of  the  successive 
steps,  we  propose  to  divide  the  entire  subject  into  the  follow- 
ing special  considerations : 

1.  An  Analytical  View  of  Logic. 

In  this  we  regard  the  science  in  its  aim  and  its  workings, 
and  after  thus  showing  its  design  and  its  scope,  we  analyze  or 
dissolve  it  into  its  different  parts,  showing  what  those  parta 
are  which  effect  by  their  combination  the  purpose  designed. 

2.  A  Synthesis  of  Formal  Logic. 

As  Synthesis  is  the  reverse  process  of  Analysis^  and  as  an 
Analysis  of  such  a  study  would  be  in  reality  but  a  general 
view  of  the  scope  of  that  science  which  Synthesis  is  to  estab- 
lish, we  shall  see  that  while  our  analytical  view  of  Logic  may 
be  brief  and  general,  )ur  synthesis  must  be  minute  and  care- 


28  LOGIC. 

ful.  We  must  more  particularly  examine  those  parts  which 
our  analysis  has  given  us,  in  order  that  we  may  be  able  duly 
to  combine  them  in  their  just  relations. 

In  imparting  instruction  upon  subjects  which  are  known, 
the  synthesis  is  evidently  the  more  important  process,  and 
hence  must  be  longer  and  more  minute,  while  in  the  inves- 
tigations of  an  unknown  science  the  analysis  is  the  more 
important  and  valuable  process. 

In  the  general  synthesis  of  Logic  we  shall  also  devote  a 
chapter  to  the  subject  of  Fallacies,  and  then  consider  some 
of  the  ways  in  which  the  syllogism  is  used,  and  the  technical 
phrases  which  express  these  uses. 

3.  A  HisTOEicAL  View  of  Logic. 

This  historical  view  of  Logic  has  been  placed  after  the 
study  of  the  formal  Logic,  rather  than  before  it,  as  is  usual 
in  most  treatises,  because  we  can  appreciate  a  history  only  of 
that  which  we  know,  and  we  shall  understand  much  better 
the  causes  of  error  and  the  obstacles  to  science  which  history 
gives  us  when  we  are  beforehand  aware  of  the  true  scope  and 
relations  of  the  particular  science  whose  history  is  related. 
When  we  know  what  Logic  is,  its  history  is  intelligible  and 
interesting,  and  not  otherwise. 

For  Logic  is  so  intermingled,  or  rather  entangled,  with 
other  kinds  of  philosophy  in  almost  all  of  its  principal 
epochs,  that  any  one  who  should  undertake  to  read  of  its 
adventures  in  history,  without  being  able  constantly  to  dis- 
sociate it  from  its  companion  sciences,  would  find  it  a  useless 
and  unprofitable  task. 


CHAPTER    n. 

ANALYTICAL    VIEW   OF  LOGIC. 

(11.)  The  Reasoning  Process  Analyzed. 

To  apply  the  method  of  analysis  to  the  study  of  Ia-^Ic  aa 
an  art,  we  begin  with  the  definition  already  laid  down  that 
Logic  is  the  Art  of  Reasoning. 

Reasoning  consists  in  the  combination  of  two  known  judg- 
ments to  form  a  third,  which  is  deduced  from  them.  Rea- 
soning, when  expressed  in  language,  is  called  argument 

The  ultimate  and  simple  form  of  argument,  logically  ex- 
pressed, is  the  syllogism*  In  a  more  extended  sense,  reason- 
ing covers  also  the  combination  and  succession  of  many 
arguments. 

The  syllogism  is  an  argument  consisting  of  three  proposi- 
tions, of  which  the  first  is  called  the  major  premiss,  the  sec- 
cond  the  minor  premiss,  and  the  third  the  conclusion.  This 
is  the  usual  order  of  the  premisses,  but  the  reasoning  would 
be  equally  valid  were  they  transposed. 

Major  premiss.  All  A  is  B  =  All  men  are  mortal. 
Minor  premiss.  All  C  is  A  =  All  Hindoos  are  men. 
Conclusion.     Therefore  all  C  is  B  =  All  Hindoos  are  mortal. 

Each  of  these  propositions  consists  of  two  terms,  the  subject 
and  the  predicate ;  and  the  verb  uniting  them  is  called  the 
copula.  Men  reason  to  satisfy  their  own  minds,  to  demon- 
strate truths,  or  to  refute  error,  and,  in  so  doing,  they  com- 
bine many  of  these  syllogisms,  thus  forming  compound  argu- 
ments, which  may  always  be  analyzed  into  the  simple  argu- 
ments which  compose  them.     In  a  simple  syllogism,  in  many 

*  Gw  and  ?.oyi^ofiac^  more  remotely  Acyw. 
3*  29 


30  LOGIC. 

cases,  one  or  other  of  these  premisses  conveys  a  fact  so  well 
known  that  it  may  be  taken  for  granted,  and  so  it  is  sup- 
pressed, and  thus  is  formed  an  abridged  argument,  called  an 
eiUhymeme.     For  example : 

{Minor  premiss)  Csesar  was  a  man, 
Therefore  Csesar  was  mortal. 

This  is  an  enthymeme  with  the  major  premiss  suppressed. 
This  major  premiss  is.  All  men  are  mortal,  which  is  taken  for 
granted  in  the  conclusion,  where,  because  Ccesar  was  a  man, 
it  is  affirmed  that  he  was  mortal.  In  every  case,  however,  if 
the  enthymene  appear  at  all  doubtful,  the  suppressed  premiss 
may  be  written  out,  and  the  validity  or  invalidity  of  the  argu- 
ment thus  determined.  Compound  arguments,  instead  of  hav- 
ing each  syllogism  fully  expressed,  are  usually  formed  of  a 
number  of  enthymemes  combined. 

The  groundwork  of  the  syllogism  is  the  dictum  of  Aristotle, 
or  his  universal  test  for  Argument. 

Without  in  this  place  entering  even  very  briefly  into  the 
History  of  Logic — a  history  of  experiment  and  error — it  is 
interesting  to  know  the  time  of  its  first  decided  manifestation, 
and  the  person  to  whom  we  owe  it  as  a  definite  science.  In 
that  magnificent  period  when  the  school  of  Plato  had  prepared 
the  mind  of  Greece  for  the  coming  of  Aristotle,  and  the 
energy  of  Philip  had  opened  the  way  for  the  conquests  of 
Alexander,  that  system  of  Logic  was  formed,  which,  after 
having  passed  through  the  fiercest  ordeals,  has  remained 
almost  without  change  to  our  day.  It  has  been  indeed  cov- 
ered up,  and  to  all  appearance  lost,  in  the  times  of  European 
bigotry  and  ignorance;  schoolmen  and  churchmen  have 
alike  assailed  it ;  but,  with  the  vital  principle  of  truth,  it  has 
remained  untouched  by  the  ruinous  hand  of  Time,  amid 
exploded  systems  of  Ethics,  false  speculations  of  Philosophy, 
and  the  cunning  allegories  of  Heathen  mythology.  The 
Analytics  of  Aristotle  form  the  cyclopaedia  of  Logic  in  thia 
age,  as  in  all  former  periods. 


THE    DICTUM    OF    ARISTOTLE. 


31 


A  fter  many  years  of  patient  investigation  Aristotle  estab- 
lished the  ''Dictum  de  omni  et  nullo"  of  which  the  first  part; 
de  omni,  refers  to  all  affirmative  reasoning,  and  the  second, 
de  mdlo,  to  all  negative  reasoning.  Stated  by  the  use  of 
T)rdiuary  symbols  it  would  be  written  as  follows : 

The  Dictum  of  Aristotle. 


De  omni. 
All  A  is  B. 

(1)         (2) 

All  or  some        C  is  A. 

(1)  (2) 


De  nullo. 
No  A  is  B. 

(1)        (2) 

All  or  some  C  is  A. 

(1) 


Therefore  all  or  some  C  is  B.  Therefore  no  C  is  B,  or  some  C 

(2) 
ie  not  B. 

Writing  out  the  forms  separately,  we  have — 

De  omni. 


(1) 
All  A  is  B. 
AU  C  is  A. 
All  C  is  B. 


(2) 
AllAisB. 
Some  C  is  A. 
Some  C  is  B. 


(3) 
No  A  is  B. 
All  C  is  A. 
No  C  is  B. 


De  nuUo. 


(4) 
No  A  is  B. 
Some  C  is  A. 
Some  C  is  not  B. 


Or,  if  stated  by  a  geometrical  notation,  as  all  syllogisms 
may  be  stated : 


But  to  explain  the  dictum  practically,  it  has  been  trans- 
lated thus : 


32  LOGIC. 

Whatever  may  be  predicated  of  a,  whole  class,  may  also  5« 
predicated  of  all  or  any  of  the  individuals  contained  in  thai 
class. 

To  predicate  *  means  to  affirm  or  deny. 

Thus  in  the  dictum  de  omni.  In  the  major  premiss  we 
predicate  or  affirm  B  of  the  whole  class  A. 

In  the  minor  premiss  we  assert  that  all  or  some  C  is  an 
individual  or  a  number  of  individuals  included  under  the 
class  A. 

And  in  the  conclusion  we  predicate  B  of  the  individuals, 
as  we  did  in  the  major  premiss  of  the  whole  class  to  which 
they  belong. 

This  simple  dictum  of  Aristotle  is  the  groundwork  of  the 
syllogism,  and  the  syllogism  is  the  universal  principle  of  rea- 
soning. It  is  sufficient  in  this  place  to  state  the  fact ;  it  will 
be  proven  hereafter.  The  propositions  of  which  the  syllo- 
gism is  composed  are  further  analyzed.  A  proposition  con- 
sists of  two  terms  and  a  copula,  of  which  the  first  term  is 
called  the  subject,  the  last  the  predicate,  and  the  connection 
between  them  is  the  copula. 

svbj.  cop.  predic. 

(Men)  (are)  (mortal) 

subj.  cop.              pred. 

(Men)  (are  not)         (trees) 

It  has  been  said  that  the  dictum  of  Aristotle  is  the  ground- 
work of  the  syllogism,  and  that  the  syllogism  is  the  universal 
principle  of  reasoning :  it  must  be  also  remarked  that  every 
valid  argument,  no  matter  what  may  be  its  original  form^ 
may  be  put  under  the  form  of  the  syllogism,  and  to  it  in  that 
form  the  dictum  may  be  directly  applied ;  and,  on  the  other 
hand,  if  any  argument  cannot  be  reduced  to  this  form,  it  is 
invalid.  Thus  this  dictum  forms  not  only  the  vehicle  of  cor 
rect  reasoning,  but  is  a  sure  test  of  error  in  Logic.     We  shall 

*  Prcedico — are. 


THE    DICTUM    OF    ARISTOTLE.  33 

coustautly  recur,  in  considering  every  form  of  argument,  to 
this  test. 

The  reasons  why  in  mathematical  investigation  we  use  let- 
ters, and  in  arithmetic  numbers,  are— first,  to  expedite  and 
simplify  the  work,  and  secondly,  to  generalize  it  For  the 
same  purposes  we  use  symbols  in  Logic.  If,  for  example,  I 
write  the  syllogism 

All  good  men  are  happy  ; 
John  is  a  good  man. 
Therefore,  John  Ls  happy, 

I  limit  my  argument  entirely  to  the  particular  of  John  being 
a  good  man  and  being  happy,  whereas,  if  I  write 

AU  AisB; 
C  is  A, 
Therefore,  C  is  B, 

I  propose  a  general  formula  which  will  apply  to  many 
cases  according  to  the  subject  and  the  matter  of  inquiry.  It 
will  be  well  for  the  student  to  frame  particular  examples 
under  the  general  formula,  and  thus  at  once  to  fix  the  form 
in  the  mind  and  accustom  himself  to  the  practical  applica- 
tions of  the  system  of  Logic  to  particular  cases. 

Besides  the  dictum  of  Aristotle,  to  the  form  of  which  every 
valid  argument  may  be  reduced,  there  will  be  given  hereafter 
a  series  of  rules  for  detecting  fallacy  and  for  determining  the 
validitv  of  an  argument  when  it  is  not  exactly  in  this  form, 
and,  by  means  of  these,  the  logical  student  may  defend  him 
self  against  the  subtlest  sophistry,  holding  Aristotle's  dictum 
in  reserve  as  a  final  test.  Where  one  who  is  ignorant  of  Logic 
is  oblised  to  use  much  eflfort  and  circumlocution  to  determine 
the  validity  of  invalidity  of  an  argument,  and  is  in  great  dan- 
ger of  error  in  the  process,  the  logician,  at  once  and  without 
inquiry  into  the  subject-matter  of  discourse,  applies  his  testa 
to  the  framework  of  the  reasoning,  and  indicates  infallibly 

C 


34  LOGIC. 

the  defect  in  the  argument.  And  so  deciding  as  to  the  valid- 
ity or  invalidity  of  the  general  formula  as  expressed  by  the 
symbolical  letters  A,  B,  C,  he  has  once  for  all  decided  for 
each  particular  example  which  can  fall  under  that  formula. 

In  concluding  this  brief  analysis  of  Logic,  let  us  recapitu- 
late. Logic  is  the  Art  of  Reasoning.  There  is  but  a  single 
universal  principle  of  Reasoning.  Reasoning  here  includes 
the  consideration  of  terms,  considered  either  as  intuitions  or 
conceptions,  their  combination  by  the  judgment  into  propo- 
sitions of  various  kinds,  an^  the  union  of  propositions  into 
arguments  as  premisses  and  conclusion.  All  these  processes 
are  conducted  in  accordance  with  the  laws  of  thought.  The 
basis  of  reasoning  is  the  dictum  of  Aristotle,  and  its  simple 
form  is  the  syllogism. 

The  syllogism  is  composed  of  two  premisses  and  a  conclu- 
sion; each  of  these  is  a  proposition,  and  each  proposition 
consists  of  three  parts,  two  terms  and  a  copula.  It  is  now 
our  purpose  to  examine  these  constituents  of  Logical  formulae 
in  the  inverse  order,  beginning  with  terms. 


Of    THE  \ 

UNIVERSITY    ) 
/ 


CHAPTER    III. 

A  SYNTHESIS  OF  LOGIC. 

{12.)  Of  certain  Operations  and  States  of  the  Mind  in 
the  Process  of  Argument. 

In  proceeding  to  the  syu thesis  of  the  reasoniug  process,  \vc 
Qiust  first  consider  certain  operations  and  states  through  which 
the  mind  passes  in  approaching  an  argument.  Logicians 
have  enumerated  many  which  are  so  nearly  related  to  each 
other  that  we  may  reduce  them  to  three : 

These  are :  1st.  Apprehension ;  2d.  Judgment ;  3d.  Beason- 
ing,  or  Ratiocination.  As  a  preparation  for  these  in  their 
order,  Attention  has  been  called  the  primary  state.  Attention 
is  not  a  distinct  faculty,  but  an  act  of  will  subordinate  to 
intelligence — a  general  phenomenon  of  intelligence ;  but  this  is 
self-evident.  Apprehension  is  a  pure  conception  of  an  object, 
whether  as  perceived  by  the  senses  or  otherwise  presented  to 
the  mental  consciousness.  The  idea  or  notion  of  the  object 
is  the  fruit  of  this  operation  of  the  mind. 

By  the  five  senses  of  the  body  we  have  a  knowledge  of  the 
world  around  us ;  the  first  step  in  obtaining  this  knowledge 
is  sensation,  or  the  impression  on  the  organ  of  sense ;  sensation 
is  conveyed  in  a  mysterious,  inexplicable  manner,  to  the  mind, 
to  produce  perception  ;  and  as  soon  as  we  have  perceived  the 
object  by  this  union  between  the  mind  and  the  senses,  the  -ah- 
ject  is  apprehended  or  taken  hold  of  by  the  mind,  and  the 
idea  is  formed  or  an  intelligent  knowledge  of  it  is  produced. 

Ideas  are  simple  or  complex. 

A  Simple  idea  is  the  notion  of  one  object,  or  of  several 
which  bear  no  relation  to  each  other ;  and  this  notion  is  ex- 
pressed generally  by  one  word,  as  John,  man,  river;  or  by 

35 


86  LOGIC. 

many  connected  by  conjunctions,  John  and  Peter ^  the  man  and 
the  boy. 

A  Complex  idea  is  the  notion  we  form  of  several  objects 
which  bear  a  relation  to  each  other,  as  a  man  walking,  a  bun- 
dle of  rods. 

When  an  idea  produced  by  an  act  of  Apprehension  is  ex 
pressed  in  language  it  is  called  a  term. 

But,  whereas  certain  words,  which  express  terms,  are  equiv 
ocal  or  ambiguous,  it  must  be  observed  that  Logic  deals  only 
with  general  or  abstract  terms,  and  has  nothing  to  do  with 
their  distinctness  or  indistinctness.  It  only  takes  for  granted 
that  a  term  is  distinct  and  unambiguous.  A  Logical  term  is 
the  expression  in  language  of  an  idea  obtained  by  act  of 
apprehension. 

2.  Judgment. 

Judgment  is  that  operation  of  the  mind  by  which,  if  we 

have  two  objects  of  apprehension  or  terms,  both  known  to  us, 

we  declare  that  they  agree   or  disagree   with   each   other. 

Thus,  if  I  know  who  "John''  is  and  what  "a  hero"  is,  I  may 

declare  that — 

John  is  a  hero, 
Or  that — John  is  not  a  hero. 

Judgment  is  therefore  of  two  kinds — affirmative  when  the 
two  terms  are  declared  to  agree,  and  negative  when  they  are 
declared  to  disagree. 

An  act  of  Judgment,  when  expressed  in  language,  is  called 
a  proposition. 

And  here  also  it  must  be  observed  that  Logic  only  takes 
cognizance  of  abstract  propositions,  which  are  expressed  by 
logical  formulae,  and  has  nothing  to  do  with  their  truth  or 
falsity;  or  rather,  it  takes  for  granted,  indeed,  that  when  a 
proposition  is  stated  it  is  true. 

For  example,  if  the  proposition  be  J.  is  B,  it  is  assumed 
by  Logic  that  A  is  in  reality  B,  and  thus,  if,  when  this  gen- 


OPERATIONS   OF    THE    MIND    IN    REASONING.  37 

eral  formula  be  translated  into  a  particular  proposition,  it 
prove  to  be  false,  Logic  is  not  responsible  for  the  falsehood, 
nor  for  the  error  which  finds  its  way  into  an  argument  by 
reason  of  the  use  of  a  false  premiss.  Much  error  has  arisen 
through  the  mistake  of  supposing  that  Logic  had  to  do  with 
Language  directly,  and  with  the  judgments  expressed  in  lan- 
guage ;  but  it  is  just  such  an  error  as  would  lead  us  to  assign 
such  values  to  the  unknown  quantities  in  any  algebraic  for- 
mula, such  for  instance  as  y^  —  Ipx  =  0,  as  would  destroy 
the  equation.  Algebra  presupposes  the  equation  to  be  just, 
and  develops  only  such  values  of  x  and  y  as  will  establish  it. 
The  Logical  formula  is  as  aostract  and  general  as  this,  and 
Logical  propositions  are  always  assumed  as  true. 

3.  Ratiocination. 

Ratiocination  is  that  act  of  the  mind  by  which,  having  two 
or  more  acts  of  judgment,  or  propositions,  we  pass  to  another 
or  others  founded  upon  them  and  growing  out  of  their  com- 
bination. 

Thus,  if  we  have  the  two  propositions 

All  men  are  mortal, 
Coesar  was  a  man, 

we  have,  as  an  inference  or  fact  implied  in  these  two  proposi- 
tions, and  deduced  from  their  combination,  the  final  proposi- 
tion Ccesar  was  mortal. 

All  act  of  ratiocination,  when  expressed  in  language,  is 
called  an  argument;  and  an  argument,  when  reduced  to  its 
simple  logical  form,  is  called  a  syllogism.  That  simple  logical 
form  demands  a  certain  order  in  the  premisses  and  the  crn- 
elusion. 

If  now  we  examine  the  syllogism 

Major  Premiss.  A  is  B  =:  Men  are  mortal, 
Minor  Premiss.  C  is  A  =  Csesar  is  a  man, 
Omrhision.         C  is  B  =  Caesar  is  mortal. 


38  LOGIC. 

we  shall  perceive  that  it  consists  of  three  propositions,  which 
are  called  the  major  and  minor  premisses  and  the  conclusion, 
and  three  terms  represented  by  A,  B  and  C,  each  term  being 
used  twice  in  the  syllogism.  The  term  which  occurs  in  the 
major  premiss  and  the  conclusion  (B)  is  called  the  major 
term ;  that  which  occurs  in  the  minor  premiss  and  the  con- 
clusion (C),  the  minor  term,  and  that  which  is  found  in  both 
premisses  (A),  the  middle  term.  The  major  term  is  always 
the  predicate  of  the  conclusion,  and  the  minor  term  the 
subject. 

Extended  ratiocination  is  conducted  by  the  combination 
of  many  of  t)  ese  syllogisms  or  their  conclusions,  according  to 
Logical  laws 


CHAPTER   IV. 

(13.)  Of  Terms. 

A  TKRM  has  been  defined  an  idea  expressed  m  language 
and  may  be  either  simple  or  complex.  As  we  shall  see  here- 
after, two  terms  are  connected  in  a  proposition,  and  the  name 
is  derived  from  this  fact,  since  they  constitute  the  termini  or 
boundaries  of  a  proposition. 

A  simple  term  expresses  a  single  object  of  apprehension, 
and  is  generally  one  word,  as  inan,  house,  field. 

A  complex  term  is  the  expression  of  several  objects  of 
apprehension  with  the  relation  which  they  sustain  to  each 
other,  as  a  good  hoy,  a  horse  running. 

It  is  evident  that  the  term  itself  is  arbitrary,  and  of  use 
only  to  convey  the  apprehension  to  another,  as  in  different 
languages  the  terms  which  express  the  same  object  of  appre- 
hension will  be  different  words;  thus  we  have  the  object 
we  call  horse  expressed  in  French  by  the  word  cheval,  and 
in  Spanish  by  the  word  cahdllo.  Words,  then,  it  must  be 
remembered,  are  not  acts  of  apprehension,  but  are  arbitrary 
signs  for  expressing  them. 

But  language,  or  the  use  of  words,  is  necessary  to  the  form 
3f  reasoning,  as  no  reasoning  can  be  applied  and  tested  until 
it  assumes  the  dress  of  language. 

When  a  word  is  capable  of  being  used  alone  as  a  term,  ii 
is  said  to  be  Categorematic,*  and  when  it  needs  the  assistance 
of  other  words  to  constitute  with  it  a  term,  it  is  called  Synca- 
ieg(yrematic.  Thus  man,  harse,  John,  are  categorematic  words ; 
here,  gave,  and,  are  syncategorematic. 

*  KaTTiydprifia  =:  something  alleged  or  affirmed. 

39 


40  LOGIC. 

By  a  casual  examination  of  the  different  parts  of  speecL 
we  shall  find : 

1st.  Of  the  noun :  That  it  is  only  categorematic  when  in 
the  nominative  case;  the  possessive,  man's,  requires  another 
word  denoting  the  thing  possessed,  and  the  objective  a  word 
which  governs  it. 

2d.  Of  the  adjective :  That  it  is  syn categorematic ;  for 
although  we  say  John  is  good,  we  understand  man  or  boy 
after  good. 

3d.  Of  the  verb :  That  it  is,  so  to  speak,  more  than  catego- 
rematic, or  hypercategorematic,  since  it  contains  often  the  copula 
and  the  predicate :  as,  the  man  walks ;  in  this  sentence  walks 
is  equivalent  to  is  walking,  in  which  is  is  the  copula,  and 
walking  the  predicate. 

The  infinitive  mood  is  often  in  reality  not  a  verb,  but  a  noun 
in  the  nominative  case.  Thus  the  sentence  To  die  for  one's 
country  is  happiness,  means  Death  for  one's  country  is  happi- 
ness ;  To  die  being  fully  expressed  by  Death. 

4th.  Of  the  remaining  parts  of  speech  we  see  at  a  glance 
that  they  are  syn  categorematic,  and  are  only  used  in  connec- 
tion with  other  words  to  constitute  terms.  The  word  which 
has  the  form  of  the  present  participle  is  sometimes  an  infinitive, 
and  sometimes  a  noun;  we  might  substitute  it  in  the  last 
example  given  as  a  case  of  either.  Dying  for  one's  country  is 
happiness,  is  equivalent  to  both  the  forms  given. 

(14.)  Division  of  Simple  Terms. 

Simple  terms  are  divided  into  singular  and  common. 

A  singular  term  is  that  which  expresses  a  single  individ- 
ual, and  is  usually  the  name  of  a  person,  place,  or  thing ;  as 
John,  Philadelphia,  the  Delaware. 

A  common  term  is  that  which  expresses  any  individual  or 
individuals  of  a  whole  class ;  as  a  man,  the  men,  an  army. 
To  make  a  common  term  singular,  we  prefix  the  demonstra- 
tive pronoun  this  or  that,  as  this  man,  that  river,  which  is 
equivalent  to  stating  the  name  of  the  man  or  river ;  as,  Thi» 


DIVISION    OF    SlMn.K    TERMS.  41 

man  is  John;  That  river  is  the  Delaware.  Common  terms 
stand  for  classes,  and  are  sometimes  called  appellative,  aa 
giving  name  or  appellation  to  many  individuals. 

They  thus  are  of  great  aid  to  science,  in  that,  when  many 
common  properties  have  been  discovered  in  a  great  number 
of  individuals,  and  their  distinctive  peculiarities  have  been 
discarded,  they  may  all  be  called  by  one  name,  and  that  name 
will  be  a'  common  term  ;  when  this  is  in  view  a  common  term 
is  called,  according  to  its  comprehension,  genus  or  species. 

Common  terms  are  further  distinguished,  according  to  their 
matter,  into  abstract  and  concrete. 

An  abstract  term  is  an  ideal  word,  expressing  an  abstract 
property  capable  of  inherence  in  an  object,  and  yet  without 
reference  to  that  object.  Thus  hardness,  length,  beaidy,  are 
abstract  terms,  which  inhere  in  many  objects,  but  do  not  indi- 
cate any  particular  one. 

A  concrete  term  is  one  which  presents  to  the  mind,  at  once, 
the  property  and  the  existence  of  the  object  in  which  it 
inheres.  Thus  hard,  long,  beautiful,  are  concrete  terms,  im- 
plying certain  objects  which  are  hard,  long,  or  beautiful. 

Concrete  terms  are  also  called  denotative  and  connotative, 
because  they  denote  the  abstract  property,  while  they  connote 
or  imply  in  their  signification  the  body  or  object  to  which  it 
belongs.  Thus  hardness,  being  an  abstract  term,  is  also  an 
ideal  noun ;  the  mind  rests  upon  the  vague  idea,  because  it 
indicates  nothing  farther;  but  when  hard  is  mentioned  we 
feel  the  right  to  ask,  what  is  hard?  the  answer  is — stone. 
Thus  the  concrete  term  hard  has  denoted  the  quality  of  hard- 
ness, and  connoted  stone  as  the  object  in  which  that  quality 
inheres. 

Terms  are  also  divided  into  absolute  and  relative.  An 
absolute  term  is  one  which  does  not  refer  to  any  other. 

A  relative  term  is  one  which  refers  to  or  implies  another. 
Two  terms  which  have  a  necessary  relation  to  each  other  are 
called  correlatives.  Thus  father  and  son,  king  and  subject, 
brother  and  sister,  are  correlatives.     Sometimes  one  term  hm: 

4  * 


42  LOGIC. 

several  relations,  or  more  than  one  correlative.  Thus  nepheit 
implies  uncle  or  aunt,  and  the  brotherhood  of  father  or  mother 
with  sister  or  brother. 

(16.)  Quality  and  Quantity  of  Terms. 

Terms  are  further  divided  according  to  their  quantity  and 
quality. 

The  quantity  of  a  term  expresses  how  much  of  it  is  taken 
or  considered. 

The  quality  of  a  term  is  the  mode  or  manner  in  which  it 
expresses  an  idea  of  an  object. 

Quality  is  essential  or  accidental.  An  essential  quality  is 
that  without  which  we  cannot  conceive  of  the  existence  of 
the  object ;  such  as  sense  and  intelligence  in  man ;  lengthy 
breadth,  and  other  dimensions  in  body. 

An  accidental  quality  is  one  which  the  object  may  have  at 
one  time  and  not  at  another ;  as  whiteness  in  a  wall ;  health 
to  the  body. 

Terms  are  said  to  be  synonymous  under  this  division,  when 
they  express  the  same  act  of  apprehension ;  but  by  common 
usage  this  exact  meaning  is  departed  from,  and  synonymous 
terms  now  mean  those  which  express  different  shades  of  mean- 
ing; thus  happiness  and  felicity  are  synonymous  terms,  and 
yet  their  etymology  teaches  us  a  difference  in  their  meanings  ; 
the  former  attributing  pleasure  to  luck  or  fortune,  and  the 
latter  simply  asserting  a  state  of  unalloyed  pleasure. 

Incompatible  terms  are  those  which  cannot  be  used  as  pre- 
dicates of  the  same  subject  at  the  same  time :  thus  hot  and 
cold ;  asleep  and  awake. 

Positive  terms  are  those  which  state  the  real  existence  of 
the  objects  they  stand  for.  The  opposite  of  these  are  negoj- 
live  terms,  or  those  which  deny  the  existence  or  assert  the 
absence  of  certain  objects  or  attributes. 

There  is  a  class  of  terms  called  Privative,  which  are  often 
confounded  with  negative  terms ;  but  there  is  a  real  and  im- 


QUALITY    AND    QUANTITY    OF    TERMS.  43 

portaut  difference  between  tliem.  A  privative  term  expresses 
that  some  quality  or  attribute  usually  belonging  to  the  class 
is  wanting  in  some  individuals  of  that  class :  thus  dumb, 
idiotic,  are  privative  terms,  since  their  very  names  call  to  the- 
mind  the  fact  that  man  generally  is  gifted  with  speech  and 
reason,  while  negative  terms  denote  the  absence  of  a  quantity 
or  property  which  is  not  due  to  the  subject. 

Terms  are  divided  according  to  their  quantity  into  many 
distinct  classes,  expressing  their  number  and  dimensions. 

Thus  we  have  the  common  division  of  numeral  and  ordi- 
nal, as  twenty,  a  hundred,  two;  positive  (in  its  grammatical 
sense),  comparative  and  superlative  terms,  as  good,  better,  best. 

That  which  is  more  truly  a  logical  division  is  into  distributed 
and  undistributed :  a  distributed  term  being  one  the  whole  of 
which  is  considered,  and  an  undistributed  term  one  of  which 
only  a  part  is  taken,  this  part  being  usually  an  indefinite  part, 
expressed  by  such  words  as  some,  few,  several,  etc.  All  nun 
is  a  distributed  term,  some  men  an  undistributed  term. 


CHAPTER   V. 

OF  THOSE   OPERATIONS  IN  LOGIC   WHICH   RELATE    TC 

TERMS. 

(16.)  Abstraction  and  Generalization. 

Cognitions,  Intuitions  and  Conceptions. — A  cognitimx 
is  the  impression  which  an  object  makes  upon  our  mind,  so 
that  we  know  it. 

An  intuition  is  the  knowledge  or  cognition  we  have  of  a 
single  object,  as  this  house ;  the  State  house ;  John,  the  Hudson. 
The  mind  receives  an  intuition,  by  simply  attending  to  the 
object.    This  is  a  technical  use  of  the  word  intuition. 

A  conception  {con  and  caper e)  is  a  notion  formed  by  gather- 
ing several  objects  into  one,  as  river,  man,  house. 

Conceptions  are  formed  by  the  processes  of  abstraction  and 
generalization. 

Abstraction  consists  in  drawing  off  and  considering  one  or 
more  ^f  the  properties  of  an  object  to  the  exclusion  of  the  rest. 
Thus  we  use  abstraction  when  we  observe  the  color  and  odor 
of  the  rose,  disregarding  its  other  characteristics.  If  we  ab- 
stract the  color  and  odor  of  one  flower,  then  of  another,  and 
so  of  many,  and  finding  these  alike  for  all,  call  them  all  by 
one  common  name  Eose,  we  are  said  to  generalize.  Abstrac- 
tion aids  us  in  passing  from  the  confused  and  complex  to  the 
distinct — always  dividing  and  simplifying  :  it  is  both  positive 
and  negative,  considering  one  or  more  by  the  negation  of 
others. 

Generalization,  then,  consists  in  disregarding  the  differ- 
ences between  ma7iy  objects  which  are  alike  in  certain  properties, 
only  considering  those  which  are  alike  and  calling  them  by  a 

44 


SPECIES,    WENUS    AND    DIFFERExNTIA.  45 

common  name — and  thus  it  is  that  general  and  universal  ideas 
are  obtained. 

We  may  abstract,  it  is  evident,  without  performing  the 
other  process  of  generalizing,  but  we  cannot  generalize  with- 
ut  first  abstracting  :  in  the  general  case,  however,  we  abstract 
for  the  purpose  of  generalizing.  It  is  by  these  two  processes 
that  we  obtain  common  terms,  or  the  names  of  classes.  All  these 
common  terms  are  the  result  of  higher  or  lower  processes  of 
generalization.  Thus,  by  a  low  generalization,  we  obtain  tea- 
rose,  by  a  higher,  rose,  by  a  higher  still,  flower,  and  by  one 
step  farther,  vegetable,  etc.  But  common  terms,  as  classes,  are 
further  distinguished  into  species  and  genera;  and,  as  expres- 
sive of  certain  things  belonging  to  the  species  and  genus,  they 
are  also  divided  into  the  differentia,  property,  and  accident. 
Some  writers,  in  considering  the  substance  of  a  term,  have 
called  the  object  for  which  it  stands,  the  essential  part  or  the 
essence. 

A  class  denoted  by  a  common  term  may  be  considered  ac- 
cording to  its  intension  or  extension.  By  intension  (also  called 
comprehension)  is  meant,  the  inclusion  of  fewer  objects  with 
more  specific  differences ;  and  by  extension,  the  inclusion  of  a 
greater  number  of  objects  with  fewer  specific  differences. 
Thus  a  species  has  more  intension  than  its  genus,  the  genua 
more  extension  than  its  species. 

(17.)  Species,  Genus  and  Differentia. 

A  q)ecies  is  a  class  obtained  by  generalization,  which  in- 
cludes only  individuals  or  subordinate  classes,  and  is  itself 
included  in  a  genus  :  as  an  Arabian  horse  is  a  species  of  horse, 
horse  is  a  species  of  quadruped;  quadruped  is  a  species  of  ani- 
mal. A  genus  is  a  class  obtained  by  a  higher  generalization, 
which  comprehends  under  it  two  or  more  species ;  as  animal 
is  the  genius  alike  of  quadruped  and  biped,  quadruped  is  the 
(^mus  of  horse,  cow,  deer,  etc.,  and  biped  the  genus  of  man,  etc. 

It  is  evident  that  in  one  sense  the  species  implies  more  than 


46  LOGIC. 

the  genus ;  as,  for  instance,  if  quadruped  be  the  genu^  and 
horse  the  species,  liorse  will  contain  all  the  signification  of 
quadruped,  and  also  the  distinctive  signification  of  horse  as  to 
shape,  size,  habits,  uses,  etc. ;  which  latter  does  not  belong  to 
quadruped. 

For  this  reason  the  species  is  said  to  express  the  whole 
Cfsence  of  the  object,  while  the  genus  expresses  only  a  part  c/ 
the  essence,  and  iliat  the  material  part,  or  part  common  to  all 
the  species  under  that  genus.  Thus,  man  expresses  the  whole 
or  complete  essence  of  the  animal  so  called,  while  animal 
expresses  only  the  comprehensive  or  material  part  of  the 
essence  which  only  limits  him  to  an  animate  existence. 

The  differentia  of  an  object  is  the  formal  or  distinguishing 
part  of  that  object,  and  divides  it  from  a  class  to  which  it 
does  not  belong ;  and  when  united  with  the  gemis  or  material 
part,  or  part  common  to  all,  forms  with  it  the  species,  or  whole 
essence.     Thus,  if  man  be  the  species,  and  animal  the  genus, 

(species) 

rational  would  be  the  differentia,  and  we  should  have  man  = 

(dififerentia)     (genus) 

rational  animal ;  by  which  it  appears  that  although  the  ex 
tension  of  the  genus  includes  this  species  and  many  others,  the 
species  really  comprehends,  although  in  a  different  sense,  more 
than  the  genus — namely,  the  genus  and  differentia — while  the 
genus  expresses  only  the  material  part,  or  that  common  to  all. 
The  genus  has  greater  extension,  i.  e.,  extends  to  more  classes 
and  individuals ;  but  the  species  has  more  comprehension  or 
intension,  i.  e.,  includes  the  part  expressed  by  the  genus,  be- 
sides the  specific  difference. 

It  is  manifest  that  the  differentia  may  be  of  three  Kinds : 
generic,  as  for  instance  the  difference  between  man  and  tree ; 
specific,  as  that  between  the  different  species,  horse  and  cow ; 
and  individual,  as  between  Byron  and  Moore  as  poets ;  but 
aach  becomes,  in  reference  to  the  genus  above,  a  specific  dif 
terence 


PROPERTY    AND    ACCIDENT.  47 

(18.)  Property  and  Accident. 
Thus,  having  shown  the  rt'hitions  between  the  species,  or 
the  whole  essence,  the  genus,  anil  the  differentia,  parts  of  the 
essence,  each  of  which  is  expressed  by  a  common  term,  we 
come  to  consider  those  things  which  are  or  may  be  joined  to 
the  species  or  essence.     They  are  divided  as  follows : 

I.  Property,  which  is  joined  universally  to  the  essence,  and 
thus  must  be  asserted  as  belonging  to  every  individual  of  the 
species ;  and,  2d.  Accident,  which  is  joined  only  contingently, 
that  is,  to  one  individual  or  certain  indimduaU  of  the  species, 
and  not  to  the  whole  species. 

Property  is  of  two  kinds  :  1st.  That  which  is  universal,  or 
belonging  to  every  individual  of  the  species,  hut  not  peculiar 
to  the  species,  as  respiration,  which,  although  it  belongs  to  all 
men,  is  not  confined  to  the  species  man.  2d.  That  which  is 
universal  and  peculiar,  as  the  power  of  intelligent  speech,  which, 
while  man  as  a  species  possesses  it,  is  peculiar  to  man.  Some 
writers  have  erred  in  enumerating  a  third  kind,  viz. :  peculiar, 
hut  not  universal,  as,  for  example,  to  he  ahle  to  he  a  poet.  But 
this  violates  our  definition,  since,  if  it  belong  to  some  indi- 
viduals and  not  to  the  species,  it  ceases  to  be  a  property,  and 
becomes  an  accident. 

II.  Accident  is  something  joined  contingently  to  the  species, 
or  belonging  only  to  certain  individuals  of  it. 

Accident  is  of  two  kinds,  separable  and  inseparable.  A 
separable  accident  is  a  circumstance  Ahich  may  be  detached 
from  the  individual  without  affecting  his  identity  or  altering 
our  general  conception  of  him ;  as  John  is  walking  or  is  lying 
down ;  in  which  examples  the  accidental  circumstance  of  walk- 
ing or  lying  down  is  not  a  necessary  part  of  the  individual, 
but  may  be  detached  from  him,  so  that  we  may  still  conceive 
of  him  as  doing  neither. 

An  inseparable  accident  is  one  which  cannot  be  detached 
from  the  individual ;  as,  horn  in  Philadelphia,  born  in  1800. 

It  is  by  means  of  such  inseparable  accidents  that  a  man  is 


48  LOGIC. 

described  or  his  history  written ;  but  it  must  be  remarked  that 
this  phraseology  is  rather  convenient  than  exact,  for  as  soon 
as  the  event  which  we  call  a  separable  accident  occurs  in  the 
life  ol"  an  individual,  it  really  becomes  inseparable.  Thus,  if 
John  walked  to  the  city  on  a  certain  day,  or,  being  unwell 
afterwards,  was  lying  down  in  consequence,  we  can  no  more 
detach  these  facts  from  his  history  than  we  can  the  event  of 
nis  being  born  in  a  certain  place  and  at  a  certain  time ;  but  as 
they  are  unimportant,  we  make  no  life-record  of  them. 

Having  now  illustrated  the  meanings  of  genus,  species, 
essence,  differentia,  property  and  accident,  let  us,  for  conveni- 
ence and  clearness  of  illustration,  write  out  a  sentence  em- 
bodying all  these  uses  of  common  terms,  as  a  model  by  which 
the  student  will  easily  frame  other  examples  for  himself. 
This  sentence  will  also  embody  the  different  processes  of 
generalization. 

(property  universal 
(individual)  (species)  (differentia)    (genus)      but  not  peculiar) 

John  is  a  Man  =  a  rational  animal,  who  breathes,  has  the 

(property  universal 

and  peculiar)  (separable  accident)  (inseparable 

faculty  of  speech,  is  lying  on  the  sofa,  and  was  born  in  Phila- 

accident) 

delphia. 

The  logical  name  given  to  every  common  term  representing 
a  genus,  species,  differentia,  property,  accident,  is  predicable , 
viz.,  something  which  may  be  predicated :  no  other  terms  than 
these  are  predicable. 

(19.)  Of  the  DiflPerent  Orders  of  G-enera  and  Species. 

A  summum  genus,  or  highest  genus,  is  the  highest  class  of 
all,  and  has  no  genus  above  it. 

A  term  which  expresses  at  once  a  genus  and  a  species  is 
called  a  subaltern  genus  and  species.  For  example,  quadru- 
ped is  a  genus  of  horse  and  a  species  of  animal. 

In  the  descending  scale  from  the  summum  genus,  the  suc- 
cessive or  ""^flerior  genus  is  called  a  subaltern  genus. 


DIFFERENT  ORDERS  OF  GENERA  AND  SPECIES.       49 

111  the  ascending  scale  from  the  lowest  species,  it  is  called 
che  subaltern  species. 

When  a  genus  is  divided  into  its  species,  they  are  called 
co-ordinate  or  cognate  species,  to  indicate  that  they  are  not 
subordinate  to  each  other.  Thus,  if  quadruped  be  divided 
into  horse,  coiu,  lion,  as  representing  the  equine,  feline  and 
vaccine  races,  these  would  be  cognate  species. 

A  species  which  contains  beneath  it  no  other  species,  but 
only  individuals,  is  called  an  infima  or  lowest  species.  In  any 
scientific  investigation,  however,  ranging  between  any  two 
limits,  although  not  absolutely  the  highest  and  lowest,  it  is  usual, 
for  convenience,  to  call  the  highest  limit  named  summum 
genus,  and  the  lowest  infima  species;  as  though  we  should 
say, "  Let  A  be  the  summum  genus  and  C  the  infima  species 
during  this  investigation."  There  are  also  in  common  use 
the  phrases  proxhmun  genus  and  remote  genus,  the  first  of 
which  means  the  genus  next  above,  and  the  second  a  genus 
faiiher  removed  from  the  species  in  question.  Thus,  quadru- 
ped is  the  proximum  and  animal  the  remote  genus  of  horse. 
It  is  necessary  that  the  proximum  genus  should  be  the  genus 
next  above  the  species  in  question ;  but  the  remote  genus  may 
be  any  one  farther  removed,  and  not  necessarily  the  summum 
genus,  which  is,  of  course,  the  most  remote. 

It  must  be  observed  that  the  use  of  a  common  term,  as 
either  species,  genus,  differentia,  property  or  accident,  is  a  rela- 
tive use ;  and  because  it  is  used  with  one  of  these  significa- 
tions in  one  sentence,  this  does  not  deter  us  from  using  it 
with  quite  another  meaning  on  another  occasion.  Thus  if 
we  take  the  word  red,  we  shall  find  we  can  make  it  serve  as 
each  in  turn. 

The  color  Red  is  a  g&nus  under  which  as  species  are  ranged 
pink,  scarlet,  crimson,  vermilion,  etc.,  the  different  kinds  of 
Bed. 

Red  is  a  species  of  the  genus  color,  and  ranges  with  white, 
blue,  yellow,  etc.,  as  cognate  species. 
5  D 


60  LOGIC. 

• 

Red  is  a  differentia  of  the  "  Red  rose,"  which  distinguishes 
it  from  other  roses.  Red  is  a  property  of  blood ;  and  an 
accident  of  a  house,  separable  if  it  be  painted  red,  inseparable 
if  it  be  built  of  Red  stone.  And  thus  in  analyzing  any  sen- 
tence we  must  be  careful  to  ascertain  the  real  value  of  the 
common  terms  employed. 

(20.)  Realism  and  Nominalism. 

While  upon  the  subject  of  common  terms,  it  is  well  to  refer 
tc  the  long-standing  controversy  between  the  Realists  and  the 
Nominalists,  which,  although  it  became  strangely  intermixed 
with  theology  and  church  polity,  had  its  origin  in  the  sigjiifi- 
cance  of  a  common  term.  It  will  be  referred  to  more  at  length 
in  the  historical  view.  The  Realists  contended  that  every 
common  term  was  the  name  of  something  really  existing — that 
a  genus  and  a  species  were  real  things;  while  the  Nomi- 
nalists believed  that  we  obtained  common  terms  merely  to 
express  a  certain  inadequate,  undefined  notion  of  one  indi- 
vidual, which  we  apply  to  many,  and  that  thus  species  and 
genera  are  mere  names  that  have  in  nature  no  correspond- 
ing reality. 

It  would  seem  to  be  a  trivial  subject  for  controversy,  but 
the  more  we  examine  it  the  more  difficult  and  subtle  it  ap- 
pears. Like  many  subtle  controversies,  it  seems  to  be  of  lit- 
tle consequence  in  which  way  it  could  be  decided  ;  but  it  had, 
to  the  disputatious  Greeks  and  the  more  disputatious  School- 
men, a  charm  on  account  of  its  subtlety,  which  its  value 
could  not  secure  to  it. 

Not  to  detain  the  student,  let  us  state  the  true  nature  of 
the  question,  and  solve  the  difficulty  by  saying,  that  genera 
and  species  are  merely  universal  ideas,  and  as  such  exist 
only  in  the  mind ;  that  they  are  expressed  by  common  terms, 
but  that  they  have  a  real  foundation  in  tie  individuals  from 
which  they  have  been  acquired. 


DEFINITION    OF    TERMS.  51 

(21.)  Definition  of  Terms. 

Definition*  is  applied  to  terms  in  tlieir  logical  use,  and 
means  limiting  thetn  in  such  a  manner  as  to  distinguish  thein 
from  all  and  any  other  terms. 

As  much  error  arises  from  the  indistinctness  of  terms,  and 
the  fact  that  different  persons  employ  them  in  different  mean 
ings,  just  definitions  which  may  bind  both  parties  in  a  con- 
troversy are  very  important, 

A  definition  is  usually  put  in  the  form  of  a  categorical 
proposition,  of  which  the  subject  is  the  term  to  he  defined,  and 
the  predicate  is  the  definition  proper.  Thus  in  the  example 
''Man  is  a  rational  animal,"  the  whole  sentence  is  called  the 
definition.  This  is  not,  however,  strictly  speaking,  correct ; 
as  the  predicate  alone,  "rational  animal,"  defines  "man,"  as 
if  in  answer  to  the  question  "  what  is  the  definition  of  man?" 

The  first  division  of  definition  is  into  two  kinds,  essential 
and  accidental.  Essential  definitions  are  further  divided  into 
physical  and  logical. 

The  second  division  of  definition  is  into  nominal  and  real. 
Before  explaining  the  meaning  of  these  divisions,  we  shall 
arrange  them,  for  the  sake  of  convenient  reference,  into  a 
tabular  statement. 

DEFINITION. 
Ist  division.  (divided  into)  2d  division. 


Essential.         Accidental.  Nominal.  Real. 

(div.  into) 


Phyfiical.  Logical 

An  essential  definition  is  one  which  presents  to  us  the  prin 
cipal  parts  of  the  essence  of  the  thing  defined ;  thus,  a  steam- 
boat is  "something  consisting  of  hull,  engine,  wheel-houses, 
smoke-pipe,  etc. ;"  or,  again,  it  is  "  a  vessel  for  water  trans- 
portation propelled  by  steam."  In  each  case  the  form  )f  our 
*  De  and  tinio,  more  remotely  jinit. 


52  LOGIC. 

essential  defiiiitioii  would  be  induced  by  the  character  of  the 
person  asking  the  definition,  and  according  to  the  information 
he  desired,  but  always  in  terms  of  the  essential  parts  of  the 
object  for  which  the  term  stands.  But  it  must  be  particu- 
larly observed  that  these  principal  or  essential  parts  are  of 
two  kinds  widely  different  from  each  other :  physical  parts 
or  parts  which  are  actually  separable  by  the  hand,  and  Logical 
parts,  or  those  w^hich  are  only  divisible  by  the  mind.  To 
explain,  a  physical  essential  definition  of  a  ship  would  be  "  an 
object  which  consists  of  hull,  masts,  cordage,"  etc.,  being  the 
parts  into  which  it  may  be  physically  divided ;  while  the 
logical  parts  which  would  constitute  a  logical  essential  defini- 
tion would  be  the  genus,  viz.,  "  ocean  vessel ;"  and  differentia, 
viz.,  "  of  peculiar  build ;"  which,  as  we  have  seen,  when  com- 
bined make  up  the  species  ship. 

(species)  (genus)  (differentia) 

A  ship — is  an  ocean-vessel — oj  peculiar  build. 

A  logical  essential  definition,  then,  in  every  case,  consists 
of  the  genus  and  differentia.  Logic  is  concerned  with  logi- 
cal definitions  alone,  but  examines  the  others  to  distinguish 
between  them  and  logical  definitions.  And  it  is  likewise  true 
that  the  physical  and  logical  definitions  sometimes  coincide, 
but  this  is  of  rare  occurrence. 

An  accidental  definition,  or  description,  as  it  has  been  tech- 
nically called,  consists  in  presenting  the  circumstances  belong- 
ing to  an  object,  and  these  are  its  property  or  accident ;  as  these 
are  generally  more  descriptive  of  an  animal  or  object  than 
the  material  part  or  part  common  to  all,  which  is  the  genus, 
or  the  differentia  which  distinguishes  the  species  in  question 
only  from  its  co-ordinate  species. 

From  what  has  been  said  before,  it  will  appear  that  in 
describing  a  species  we  can  only  use  properties,  as  accidents 
attach  alone  to  individuals,  while  properties  belong  to  every 
individual  of  a  whole  species ;  we  should  use,  besides,  proper- 
ties which  are  universal  and  peculiar,  since,  as  they  belong  to 


NOMINAL    AND    REAL    DEFINITIONS.  5»^ 

every  individual  ot  the  species,  and  to  none  out  of  it,  rve  thiw 
find  its  own  characteristics ;  whereas  if  we  used  the  proper 
ties  which  were  universal  but  not  peculiar,  we  should  only 
know  characteristics  which  marked  that  species  in  common 
with  others,  and  thus  not  define  it.  Thus  if  we  should 
describe  man  as  "a  being  who  lived  and  breathed,"  this  would 
not  define  or  describe  him  jiistly.  So,  too,  in  describing  an 
individual,  as  for  instance  in  biographical  notices,  we  should 
not  use  separable  accidents  which  are  not  a  permanent  and 
necessary  part  uf  the  object,  but  inseparable  accidents  which 
belong  necessarily  and  permanently  to  it.  For  example,  if 
we  say  "  William  was  the  Duke  of  Normandy  who  conquered 
England  in  1066,"  we  describe  him  by  means  of  the  insepa- 
rable accidents,  viz.,  that  he  was  Duke  of  Normandy,  and 
that  he  conquered  England. 

(22.)  Nominal  and  Real  Definitions. 

We  come  now  to  the  second  division  of  definitions,  into 
nominal  and  real. 

A  nominal  definition  is  one  which  gives  the  meaning  of  the 
term  which  is  used  as  the  name  of  the  thing.  In  brief,  it  de- 
fines the  name.  Thus,  "  a  telescope  is  an  instrument  for  view- 
ing distant  bodies."  "  The  photograph  is  a  painting  made  by 
light  on  sensitive  plates."  "  The  decalogue  is  the  table  of  the 
ten  commandments." 

A  real  definition  analyzes  and  explains,  not  the  name  of 
the  thing,  but  the  thing  itself;  enumerating,  besides,  all  its 
important  characteristics  and  properties;  thus,  a  real  defi- 
nition for  a  telescope  would  be  a  treatise  on  the  constniction, 
powers,  and  uses  of  the  instrument,  and  a  real  definition  of 
the  decalogue  would  be  given  only  by  reciting  all  its  command- 
ments. 

In  the  investigations  of  science  it  is  evident  tliat  the  aim 
is  to  obtain  real  definitions,  and  the  fuller  and  more  complete 
they  are  the  greater  their  value ;  but  since  in  Logic  we  have 

6  • 


54  LOGIC. 

ouly  to  do  with  the  names  of  things,  and  not  with  their  subject 
matter,  or  the  conceptions  \a  hich  they  convey  to  us,  it  is  evi- 
dent that  we  only  need  nominal  definitions  and  not  real;  and 
indeed,  with  regard  to  matters  of  general  information,  a  nomi- 
nal definition  will  be  suflicient  to  settle  the  grounds  of  a  con- 
troversy ;  for  while  it  is  the  name  that  indicates  the  individual 
or  the  class,  the  definition  explains  the  name. 

We  may  even,  sometimes,  provided  both  parties  to  an  argu- 
ment agree  to  do  so,  consider  as  a  definition  something  which 
is  purely  hypothetical,  but  which  still  partakes  of  the  nature 
of  a  definition ;  thus,  for  example,  in  an  astronomical  prob- 
lem we  say,  '^let  C  be  the  sun's  place  in  the  heavens;"  or  in 
any  case,  for  purposes  of  illustration,  "  let  so  and  so  be  so  and 
so"  This  form  of  definition  is  purely  relative ;  for  although, 
in  reality,  C  is  not  the  sun's  place,  it  is  so  relatively  to  the  other 
points  on  the  diagram. 

It  must  also  be  observed  that  it  is  not  necessary  to  the  just- 
ness of  a  definition  that  it  should  refer  to  real  things,  as,  for 
example,  we  define  an  unicorn  to  be  "  a  fabled  animal,  having 
but  one  horn,"  and  a  phoenix  to  be  "a  bird  fabled  to  live  with- 
out a  mate  and  to  rise  from  its  own  ashes" 

(23.)  Rules  for  Definition. 

So  important  has  the  subject  of  definition  been  considered, 
that  Logicians  have  laid  down  three  rules  for  it,  to  which,  if 
we  adhere,  we  shall  insure  just  and  adequate  definitions. 

1st.  The  definition  must  give  to  the  mind  a  clearer  concep- 
tion than  the  name  of  the  thing  defined,  or  it  will  be  useless. 
The  clearness  of  a  definition  is  opposed  by  negative  attributes ; 
thus  to  define  man  as  not  a  quadruped  would  be  unsatisfactory 
in  this  respect. 

In  most  of  the  arts  and  sciences  this  consists  in  putting 
a  technicality  into  plain  language,  for  those  who  are  unin- 
itiated ;  but  if  I  am  asked  to  define  cow,  a,  word  understood 
■oy  every  one,  and  say  that  cow  is  a  ruminant  quadruped,  J 


RULES    FOR   DEFINITION.  55 

violate  the  rule.  In  the  nomenclature  of  science  many  tech- 
nical terms  give,  in  one  word,  what  it  would  require  much 
circumlocution  to  express  in  common  words.  Accompanying 
this  rule  there  is  the  caution  that  the  character  of  the  defini- 
tion should  depend  upon  the  subject  an«i  the  persons  adclr*>ssed. 
2d.  The  definition  must  be  adequate ;  that  is,  neither  in- 
clude other  things  than  those  necessary  to  define,  nor  exclude 
any  necessary  explanation  of  the  thing  defined. 

Thus,  if  I  define  bird  to  be  "  an  animal  that  moves  in  the  air 
by  means  of  wings,'^  I  am  too  extensive  in  my  definition ;  as 
that  would  include  other  animals  than  birds,  as  bats,  flying 
fish,  etc. ;  and  if  I  define  it  to  be  "  a  feathered  animal  thai 
sings"  that  would  be  too  narrow,  as  some  birds  do  not  sing. 

od.  The  third  rule  is  rather  a  caution  which  grows  out  of 
the  other  two  than  a  rule  like  them.  It  is,  that  the  words 
used  in  a  definition  should  be  sufficient  and  of  the  proper  kind 
to  define  the  thing. 

If  we  use  too  many  words,  we  confuse  the  meaning  and  are 
liable  to  tautology;  if  too  few,  we  are  liable  to  obscurity. 
Thus,  to  say  that  "  a  square  is  a  four-sided  figure  with  equal 
sides,''  would  be  true  but  not  definite,  as  there  may  be  drawn 
other  parallelograms  not  right  angled,  with  equal  sides.  If 
we  say  "a  'parallelogram  is  a  four-sided  figure  whose  opposite 
sides  are  equal  and  parallel,''  we  use  too  many  words,  as  the 
equality  of  the  sides  implies  the  parallelism,  and  vice  versa. 

In  the  first  case  we  err,  because  we  do  not  exclude,  in  our 
definition  of  the  square,  all  other  figures ;  in  the  second,  be- 
cause we  allow  it  to  be  supposed  that  there  are  four-sided 
figures  whose  opposite  sides  are  equal  and  not  parallf-l 
Under  the  head  of  tautology  comes  what  is  called  Defining 
in  a  Circle ;  i.  e.,  by  using  the  term  to  be  defined  in  the  defi- 
nition. Right  is  mun's  power  to  do  or  not  to  do.  Law  is  a 
legal  ordinance;  evil  is  that  which  is  not  good. 

The  examples  taken  are  broader  and  more  apparent  than 
those  in  which  faulty  definitions  are  generally  used,  but  they 


56  LOGIC. 

rend<3r  the  error  more  obvious,  and  indicate  to  us  the  charao 
ter  of  the  danger  to  be  avoided. 

If  we  would  see  the  practical  necessity  of  definitions,  we 
need  but  consider  a  few  of  the  vague  and  inexact  terms 
which  we  use  in  our  ordinary  speech,  and  which  it  seems  a 
prevailing  fashion  to  distort  in  their  meanings.  We  shall 
recur  to  this  subject  under  the  general  title  of  "  Verbal  Fal- 
lacies," but  may  now  give  a  few  illustrations  of  the  value  of 
exact,  definitions.  Take  for  example  such  words  as  Necessity 
and  Necessary,  which  may  mean  either  an  accordance  with 
the  invariable  law  of  God,  or  an  obedience  to  the  blind  de- 
cree of  fate,  according  to  the  belief  or  skepticism  of  him  who 
uses  them.  In  its  political  sense,  the  adjective  necessary  has 
been  said  to  be  capable  of  certain  degrees  of  comparison,  as 
in  the  argument  urged  in  favor  of  the  Bank  of  the  United 
States,*  in  speaking  of  the  means  necessary  for  carrying  out 
the  provisions  of  the  Constitution,  it  was  asserted  that  they 
may  be  classed  under  the  three  categories  of  necessary,  very 
necessary,  and  absolutely  and  indispensably  necessary.  So  also 
in  religion,  certain  things  are  said  to  be  generally  necessary 
to  salvation,  while  others  are  said  to  be  absolutely  necessary. 
Thus  the  technical  sense  of  the  word  is  entirely  lost,  as  that 
refers  to  an  absolute  condition,  which  cannot  but  be,  or  canyiot 
be  otherwise,  and  therefore  does  not  admit  of  comparison. 
Or  if  we  would  see  a  strange,  conglomerate  example  of  indef- 
inite and  erroneous  terms,  demanding  a  clear  definition,  take 
the  war-cry  of  the  French  revolutionists,  ^^  Liberty,  Equality, 
Fraternity  f^  no  one  word  of  which  can  express  to  the  people 
a  distinct  idea,  or  will  bear  the  test  of  a  clear  definition. 

It  has  been  a  custom  in  nominal  definitions  to  define  one 
term  by  means  of  its  synonym,  borrowed  from  another  lan- 
guage. Although  our  language  is,  in  its  structure  and  the  great 
majority  of  its  principal  words,  Anglo-Saxon,  still  the  large 
number  of  French  and  Latin  words  which  have  been  brought 
into  it  have  formed  terms  synonymous  with  the  original  Saxon 
^'  Kent's  Commentaries,  vol  i.,  Lect.  12 


RULES    FOR    DEFINITION.  67 

but,  when  Lhey  had  become  naturalized,  as  we  had  no  use  for 
two  words  exactly  synonymous,  wisdom  suggested  that  they 
should  exhibit  shades  of  difference  in  meaning,  which  did  not 
originally  belong  to  them  •  so  that  few  if  any  words  are  justly 
defined  by  their  synonyms.  Besides,  as  a  similar  idea  among 
any  two  people  would  have  its  differences  drawn  from  the  r 
own  peculiarities  of  clime,  and  race,  and  manner  of  life  and 
government,  the  synonyms  when  brought  into  the  language 
would  often  express  great  differences  at  once,  and  without 
any  effort  on  our  part  to  cause  them  to  do  so.  As  a  remark- 
able instance  of  this,  let  us  see  how  very  wrong  it  would  be 
to  define  our  English  word  freedom  by  its  synonym  liberty, 
which  comes  to  us  from  the  Latin ;  and  yet,  how  many  con- 
found the  two.  Indeed  these  are  historic  words,  and  give  us 
an  insight  into  the  times  of  their  birth,  wonderfully  illus- 
trative of  the  people  and  countries  from  which  they  came. 
Freedom  is  the  personal,  individual  independence  and  right 
of  every  man,  his  free  doom ;  i.  e.,  free  province  or  jurisdic- 
tion from  his  birth.  Coming  as  it  does  from  the  Teutonic 
element  in  our  language,  it  tells  us  of  the  free  and  independ- 
ent Germans,  who,  by  their  own  valor,  overturned  the  great 
fabric  of  the  Roman  empire.  They  were  men  of  the  forest 
and  mountain,  inhabiting  no  cities — there  were  none  in  Ger- 
many till  after  the  eighth  century — but  only  roving  where  were 
the  lordliest  spoils,  and  claiming  them  as  the  reward  of  their 
personal  freedom.  On  the  other  hand,  liberty  tells  us  of  the 
Roman  cities,  of  the  sway  of  the  Roman  empire,  and  of 
Roman  licentiousness ;  of  a  form  of  manumission,  implying 
slavery ;  individuality  merged  into  citizenship.  To  be  a 
Roman  citizen  was  to  have  attained  the  post  of  honor,  open 
to  all  advancement  in  diplomacy  and  war.  Nor  is  the  spirit 
belonging  to  these  words  yet  lost.  While  we  cling  like  good 
citizens  to  our  liberty,  vouchsafed  to  us  by  the  constitution  of 
the  country  as  Americans,  we  much  more  desire  to  keep  well 
guarded  that  freedom  of  opinion,  of  speech,  of  action,  whidb 
is  our  indefeasible  right  as  men. 


58  LOGIC. 

In  view  of  the  importance  of  just  definitions,  let  us  under 
take  no  controversy  or  expression  of  opinion  involving  a 
vague  and  indistinct  term,  without  demanding  a  definition, 
and  agreeing  to  use  it  during  the  discussion. 

(24.)  Division. 

It  is  of  great  importance  in  the  consideration  of  common 
terms  which  stand  for  classes,  that  we  should  be  able  to  divide 
them  into  all  their  several  parts  or  significates.  An  individ- 
ual, as  its  name  indicates,*  is  incapable  of  logical  division. 
It  is  only  a  species  or  genus — i.  e.,  a  class,  in  more  general 
language — which  can  be  so  divided. 

Division  is  of  two  kinds,  physical  and  logical;  to  these 
some  writers  add,  improperly,  numerical  division. 

Physical  division,  also  called  partition,  is  the  actual  separa- 
don  of  the  physical  parts  of  which  a  thing  is  composed.  It 
is  evident  that  an  individual  is  capable  of  physical  divmon ; 
thus,  an  individual  tree,  as  a  certain  oak,  may  be  divided  into 
trunk,  branches,  and  these  further  subdivided  into  bark,  heart, 
leaves,  etc. ;  an  individual  7nan,  as  Johii,  may  be  physically 
divided  into  head,  arms,  trunk,  legs,  etc.  With  this  kind  of 
division  Logic  has  directly  nothing  to  do. 

Logical  division,  which  takes  place  in  the  mind  only  and  is 
only  applied  to  classes,  consists  in  separating  a  genus  into  its 
different  species ;  and  a  species  into  the  individuals  composing 
it ;  and  this  in  regular  order  from  the  summum  genus  to  the 
infima  species.  Thus,  the  genus  tree  would  be  logically  divi- 
ded into  oak,  maple,  hemlock,  fir,  pine,  elm,  etc. ;  and  the  species 
oak,  into  red  oak,  white  oak,  live  oak,  scrub  oak,  etc. ;  and  each 
of  these  again  into  the  individual  trees  comprising  its  kind. 

It  will  be  evident  that  in  a  just  division,  each  one  of  the 

parts — denoting  a  species — will  be  less  than  the  whole  num- 

"oer  which  make  up  the  genus;  or  any  one  of  the  parts — 

denoting  an  individual — will  be  less  than  the  whole  uumbei 

*  In  and  dividuus,  from  divide,  to  divide. 


DIVISION.  59 

which  msLi^e  up  the  species ;  or,  as  a  te&t  of  the  correctues* 
of  the  division,  we  must  be  able  to  predicate  the  siunmum 
genus  of  any  one  of  the  parts. 

If,  for  example^  we  have  assumed  tree  to  be  the  summum 
genus,  we  must  be  able  to  predicate  tree  of  oak^  or  live  oak,  or 
any  individual  live  oak. 

It  is  evident  that  the  same  term  may  be  logically  divided^ 
occonHng  to  race,  into  Caucasians,  Malays,  etc. ;  according  to 
creeds,  into  Buddhists,  Jews,  Mohammedans,  Christians,  etc. ; 
according  to  nation,  into  Americans,  English,  French,  etc. 
These  cross-divisions  must  not  be  mingled  or  confounded ; 
for  example,  to  divide  man  into  Caucasians,  Mohammedans, 
Americans,  etc.,  would  be  false  and  useless  division. 

The  principle  of  division  is  best  illustrated  by  a  scheme,  or 
inverted  tree,  in  which  are  arranged  clearly,  symmetrically,  and 
without  arbitrariness,  the  difterent  parts  of  the  division. 

SCHEME  OF  DIVISION.— SUMMUM  GENUS. 

TREE. 

^^>. ^ . 

Oak,  Maple.  Pine,  etc. 


Live  Oak,  White  Oak,  Red  Oak,  etc.  Sugar  Maple,  Common  Maple. 


Individual  Trees.  Individual  Trees. 

It  may  be  well  to  observe  particularly  an  auxiliary  phrase, 
according  to,  which  we  use  to  keep  us  from  a  simple  but  dan- 
gerous error ;  i.  e.,  every  division  should  be  governed  by  one 
and  a  single  principle.  Man  is  divided  not  into  races,  creeds, 
nations,  etc.,  but  acc(yrding  to  these,  into  various  parts,  thus : 

SUMMUM  GENUS.— MANKIND  DIVIDED  ACCORDING  TO 


Race.  Creed.  Nation. 


C«nca«iaD,  Malay,  etc.    Jews,  Christians,  Mohammedaus.    Kngiisli,  French,  German,  etc 


60  LOGIC. 

It  is  evident  that  all  the  co-ordiuate  species  must  be  on  the 
same  line  or  platform,  that  is,  they  must  hold  the  same  rela- 
tive position  to  the  summum  genus.  We  must  be  careful  to 
omit  no  subaltern  genus ;  and  we  must  place  each  subaltern 
geniLs  in  its  own  relative  grade.  Thus,  if  we  should  place 
oak  properly,  in  the  division  of  tree,  but  should  pass  immedi- 
ately from  the  genus  tree  to  the  species  sugar  maple,  thas  leav- 
ing out  the  species  maple,  co-ordinate  to  oah,  we  should  make 
an  unequal  and  undue  division.  This  would  be  placing  one 
of  the  co-ordinate  species  on  the  same  level  with  one  subordi- 
nate to  it.  In  other  words  generic,  specific  and  individual 
difierences  must  determine  the  systematic  arrangement.  To 
sum  up : 

I.  The  species  constituting  the  genus  must  exclude  one 
another. 

II.  All  the  species  taken  together  must  be  equal  to  tho 
genus  divided. 

III.  The  division  must  be  made  according  to  one  single 
principle. 

From  what  has  been  said,  it  will  be  seen  that  the  process 
of  Division  is  exactly  the  opposite  of  Generalization. 

As  in  Generalization  we  disregarded  the  differences  between 
many  individuals,  or  between  many  species,  and  considered 
only  the  properties  they  had  in  common,  that  we  might 
constitute  them  respectively  species  and  genus,  calling  them 
by  a  common  name,  so  in  Division  we  take  the  genus  thus 
obtained  and  add  to  it  the  several  differences  which  we  had 
removed  in  Generalization,  and  which  distinguish  its  parts, 
that  we  may  call  the  parts  thus  enumerated  by  separate 
names. 

The  two  inverse  processes  of  generalization  and  division  may 
be  plainly  illustrated  by  a  scheme  or  double  tree ;  and  this 
may  be  made  as  full  as  we  please :  thus,  from  individual  trees 
we  may  generalize  to  the  genus  tree;  or,  from  trees  and  shrubs 
and  other  kinds  of  vegetation,  we  may  generalize  to  the  sura 


DIVISION.  61 

mum  genus  vegetable.     The  di vision  will  be  of  the  exact  spe- 
cies, etc.,  but  iu  the  inverse  order. 

SCHEME  OF  GENERALIZATION  AND  DIVISION. 

Individual  TVees.  Individual  Trees.  Individual  Trees. 


Live  Oak,  Rad  Oak,  etc.   Sugar  Maple,  Common  Maple,  etc.  White  Pine,  Yellow  Pine,  etc. 


Oak.  Maple.  Pine. 


TREE. 


Oak.  Maple.  Pine. 


Live  Oak,  Red  Oak,  etL-.   Sugar  Maple,  Common  Maple,  etc.   White  Pine,  Yellow  Pine,  etc. 


Individual  Trees.  Individual  Trees.  Individual  Trees. 

What  has  been  called  irudhematical  or  7iumerical  division  is 
in  reality  but  a  form  of  physical  division ;  thus,  I  divide  a 
loaf  into  slices,  or  an  apple  into  pieces,  physically,  with  or 
without  regard  to  the  equality  of  the  pieces,  or  their  sizes 
relatively  to  each  other.  If  this  equality  or  relation  be  ob- 
served, it  may  be  called  numerical  division,  but  it  is  only  an 
exact  form  of  physical  division ;  as  a  half,  a  third,  ten  times 
as  great,  etc.,  etc. 

By  a  comparison  of  the  subjects  of  Division  and  Definition, 
it  will  be  seen  that  division  is,  after  all,  but  a  systematic  and 
practical  kind  of  definition,  since  there  can  be  no  better  way 
to  illustrate  the  meaning  of  tree  than  logically  to  divide  it, 
before  our  eyes,  into  all  its  species  down  to  individual  trees. 

It  will  be  readilv  seen  that  the  nature  of  the  logical  division 
of  terms  will  depend  much  upon  the  science  in  which  they  are 
used,  and  the  principle  according  to  which  they  are  to  be 
classified.  Thus,  an  ethnologist  would  divide  mankind  accord- 
ing to  races,  a  theologian  according  to  creeds,  and  a  state^wian 
according  to  nation.     The  principle  of  all  the  divisions  would 

6 


62  LOGIC. 

be  the  same,  while  the  resulting  cross-divisions,  as  we  have 
seen,  will  be  widely  different. 

(25.)  Recapitulation. 

It  will  be  well  to  recapitulate  briefly  what  has  been  said 
upon  the  subject  of  terms,  and  the  various  operations  which 
concern  them.     We  have  shown — 

1st.  That  a  term  is  the  expression  of  an  object  of  appre« 
hension,  and  have  explained  the  different  kinds  of  terms, 
according  to  a  regular  division. 

2d.  That  common  terms  are  obtained  by  the  processes  of 
Abstraction  and  Generalization. 

3d.  The  distinction  between  genera,  species  and  individuals, 
etc. 

4th.  The  Definition  of  terms,  and  just  rules  for  definition. 

5th.  Division  of  terms,  with  the  difference  between  physical 
and  logical  division,  and  special  consideration  of  the  latter. 

The  next  step  will  be  to  combine  these  terms  into  proposi- 
tions ;  that  is,  from  our  knowledge  of  two  of  them  to  assert 
Iheir  agreement  or  disagreement. 


CHAPTER   VI. 

(26.)  Propositions. 

A  proposition^  is  an  act  of  judgment  expressed  in  lang^  age 
and  consists  of  three  parts,  a  subject,  a  predicate  and  a  copula ; 
the  subject  and  the  predicate  are  called  the  terms  or  extremes 
of  the  proposition. 

The  subject,  in  the  due  order,  is  placed  first,  and  is  that  of 
which  something  is  predicated,  i.  e.,  afiirmed  or  denied. 

The  predicate  is  that  which  is  afiirmed  or  denied  of  the 
subject. 

The  copula  is  always,  in  categorical  propositions,  the  uniting 
word  which  expresses  the  agreement  or  disagreement  between 
the  subject  and  predicate,  and  is  always  some  part  of  the  verb 
to  be.  When  the  copula  is  affirmative,  agreement  is  expressed ; 
when  negative,  disagreement. 

subj.   cop.   pred.  subj.     cop.  pred. 

A     is     B  ^  (Caesar)  is  (a  tyrant). 

subj.       cop.      pred.  subj.  cop.  pred. 

A  (is  not)  B  =  (Caesar)  (is  not)  (a  tyrant). 

The  negative  particle,  it  must  be  observed,  is  always  a  pari 
of  the  copula. 

What  appear,  in  our  ordinary  speech,  to  be  simple  proposi- 
tions are  sometimes  inverted  or  elliptical  forms  of  expression, 
which  must  be  put  into  simple  logical  form  before  they  can 
be  c  nsidered  as  propositions. 

Thus  we  say  "  I  hope  to  see  you,"  "  1  desire  to  remain  ;" 
and  in  these  cases  the  subject  is  really  placed  last ;  the  true 
meaning  being 

*  From  propono,  something  proposed  or  set  fortli  for  our  accojitance 

6.S 


64  LOGIC. 

sul)j.  cop.  prod. 

{To  see  you)  is  {the  thing  which  I  hope,  or  my  hope). 

As  an  example  of  another  for^i  of  inversion,  we  have  thai 
which  springs  from  the  constant  U30  of  the  neuter  pronoun  it 

Thus,  in  ordinary  language,  we  say,  "  It  is  true  that  I  think 
so."     The  true  logical  form  may  be  given  thus : 

subj,  cop.  pred. 

(That  I  think  so)  is  (a  true  thing). 

Many  writers  have  denied  that  there  is  such  a  thing  as  a 
negative  judgment,  and  consequently  that  any  negation  at- 
taches to  the  copula ;  for  they  say  that  the  proposition  John 
is  not  happy  is  equivalent  to  John  is  unhappy,  which  transfers 
the  negation  from  the  copula  to  the  predicate ;  but  this  is  a 
quibble  about  words,  as  there  are  propositions  in  which  the 
negation  cannot  be  thus  destroyed,  and  such  is  the  case  with 
far  the  greater  number.  The  positive  term  is  generally 
limited  and  intelligible,  the  negative  unlimited  and  indefinite ; 
thus,  man  is  a  term  which  we  can  grasp,  but  not  man  includes 
all  the  universe  beside. 

Of  the  Copula. — The  copula  may  be  always  reduced  to  the 
present  tense  of  the  indicative  mood  of  the  verb  to  be,  and 
consequently  expresses  neither  pa^t  nor  future  time.  Thus, 
"  Caesar  was  the  conqueror  of  Gaul,"  is  equivalent  to  "  Caesar 
is  the  historic  personage  who  conquered  Gaul."  "  I  shall  he 
glad  to  see  you,"  is  the  same  as  "  I  am  the  person  who  will 
be  glad  to  see  you,"  etc. ;  but  as  this  reduction  is  in  general 
unnecessary,  we  agree  to  call  those  propositions  which  are 
expressed  in  time  other  than  the  present.  Very  often  the 
copula  and  predicate  are  expressed  together  in  one  word,  as 
"  The  sun  shines  ;"  here  the  word  shines  may  be  resolved  into 
is  shining,  in  which  is  is  the  copula,  and  shining  the  predicate. 
And  sometimes,  in  other  languages,  as  the  Latin  or  Greek,  a 
proposition  is  conveyed  in  one  single  word,  as  amo,  I  love  or 
I  am  loving,  tutttw,  I  am  striking ;  but  in  every  case,  a  prop- 


PROPOSITIONS.  66 

osition  may  easily  be  placed  in  such  a  form  that  the  subject, 
predicate,  aud  copula  are  distinctly  stated. 

But  this  definition  of  a  proposition,  as  a  sentence  consist- 
ing of  a  mbjed,  predicate  and  copula^  is  evidently  a  physical 
definition,  and  is  not  sufficient  for  our  purpose.  The  logical 
definition  of  a  proposition  is  "a  sentence  ivhich  affirms  or 
denies ;"  here  proposition  is  the  species,  sentence  the  genus,  and 
ivhich  affirms  or  denies  is  the  differentia,  or  statement  of  the 
difierence  between  this  kind  of  sentence  and  all  others.  The 
word  proposition  not  having  in  its  etymology  this  strict  mean- 
ing, it  is  very  loosely  used  to  express  almost  every  kind  of 
sentence.  We  must  be  careful,  in  Logic,  to  limit  it  to  the  defi- 
nition just  given.  Hence,  we  should  say  that  a  categorical 
proposition,  in  its  grammatical  sense,  implies  the  iiidicative 
mood,  since  absolute  affirmation  or  denial  is  expressed  only 
by  that  mood.  Thus  are  excluded,  the  imperative  mood  or  all 
commands,  the  subjunctive  mood  or  all  hypotheses,  the  infinitive 
mood,  which,  as  its  name  indicates,  is  not  a  fiiiite,  uniting 
verb,  but  only  a  verbal  noun. 

If  we  examine  these  moods  a  little  more  in  detail  we  shall 
find,  first,  that  even  in  the  indicative  mood,  questions,  or  the 
interrogative  form  of  that  mood,  are  excluded,  for  the  use  of 
a  question  implies  that  one  of  the  parts  of  the  proposition  is 
wanting,  and  that  we  depend  upon  the  answer  to  supply  it. 
Thus  the  first  and  simplest  form  of  the  question  is 

Is  A  B?  =  ls  man  mortal ? 

If  the  answer  be  affirmative,  then  we  have  a  right  to  the 
copula  is,  which  before  was  wanting,  and  may  write 

A  is  B  =  Man  is  mortal. 

Anoihei  form  of  the  question  is  "What  is  A?"  or  "What 
is  B?"  the  answer  to  which  will  supply  us  with  the  predicate 
and  subject  respectively.  With  regard  to  the  subjunctive 
mood    there   ai'e,   it  must   be   observed,  propositions  which 

«•  E 


66  LOGIC.  . 

assume  that  form  and  wiiich  are  called  hypothetical,  and  they 
come  under  the  class  of  compound  propositions,  as 

If  A  is  B,  CisD. 

In  almost  every  case  the  hypothesis  is  stated  in  the  indica- 
iive  rather  than  the  subjunctive  mood  ;  thus, 

If  A  is  B,  C  is  J) ;  rather  than  in  the  form  : 

If  AbeB,C  will  be  D. 

Of  the  infinitive  mood  it  may  be  observed  that  there  are 
various  forms ;  thus,  to  ride  is  pleasant,  may  be  rendered  by 
riding  is  pleasant;  horseback  exercise  is  pleasant;  plainly 
showing  that  with  the  verbal  form  there  is  a  substantive  value. 

(27.)  Propositions  Divided  into  Simple  and  Compound. 

If,  now,  we  proceed  to  consider  first  the  substa^ice  of  propo- 
sitions, we  shall  find  them  divided  according  to  their  substance 
into  simple  and  co7npound. 

A  simple  proposition  is  one  which  has  but  one  subject  and 
predicate,  united  by  the  copula  is  or  is  not.  Simple  proposi- 
tions are  also  called  categorical,  that  is,  there  is  simply 
affirmed  or  denied  an  agreement  between  the  subject  and 
predicate. 

A  compound  proposition  is  one  which  has  more  than  one 
subject  or  more  than  one  predicate,  and  may  be  resolved  into 
two  or  more  simple  propositions;  as  The  Delaware  and  the 
Schuylkill  are  rivers  in  Pennsylvania.  Compound  proposi- 
tions are  further  divided  according  to  their  substance  into 
categorical,  modal,  conditional,  causal  and  disjunctive. 

A  compound  categorical  proposition,  like  a  simple  categori 
eat,  affirms  or  denies  the  predicate  simply  and  certainly  J>f 
the  subject ;  thus, 

Alexander,  Ccesar  and  Napoleon  were  ambitious  of  military 
glory. 

A  modal  proposition  is  one  in  which  the  mode  or  mannei 
of  agreement  or  disagreement  between  the  subject  and  predi 
cate  is  stated,  as  Ccesar  conquered  Pompey  by  unfair  means. 


QUANTITY    AND    QUALITY    OF    PROPOSITIONS.         li? 

A.  conditional  proposition  consists  of  two  siinj)le  categori- 
eals  united  l)v  the  conjunction  if;  thus, 

If  A  is  B,  CisD. 

It  is  usual,  for  convenience,  to  place  the  conjunction  5rst , 
the  first  categorical — A  is  B — is  then  called  the  antecedent, 
ind  the  other — C  is  D — the  consequent. 

A  causal  proposition  is  one  in  which  the  reason  of  thf^  truth 
of  a  simple  proi)Osition  is  stated  ;  thus. 

Because  A  is  B,  C  is  D. 

A  disjunctive  proposition  is  one  in  which  one  of  two  oi 
more  simple  propositions  is  asserted  to  be  true ;  thus, 

Either  A  is  B,  or  C  is  D. 

This  is  done  by  the  use  of  the  conjunctions  either  and  or. 

Propositions  are  still  further  divided  according  to  two  of 
Aristotle's  categories  which  will  be  considered  hereafter ; 
i.  e.,  according  to  their  quantity  and  quality.  In  simple  lan- 
guage. Quantity  considers  of  how  much  of  the  subject  the 
predicate  is  affirmed  or  denied ;  as,  some  or  all  A  is  B. 

And  Quality  regards  the  kind  or  manner  of  that  predica- 
tion, i.  e.,  whether  it  be  affirmative  or  negative ;  whether  A  t^- 
or  is  not  B. 

(28.)  Quantity  and  Quality  of  Propositions. 
The  quantity  of  a  proposition  is  determined  by  the  amount 
or  portion  of  its  subject  which  we  consider.  If  we  assert 
that  the  predicate  agrees  or  disagrees  with  the  whole  subject, 
that  is,  all  the  significates  which  come  under  the  term,  the 
proposition  is  said  to  be  udversal;  thus, 

A II  men  are  mortal,  no  men  are  trees, 

are  universal  propositions,  because  the  whole  of  the  subject  is 
considered.  B'lt  if  we  assert  the  predicate  to  agree  or  to  dis- 
agree with  only  a  jxirt  of  the  subject,  the  proposition  is  called 
particular. 


68  LOGIC. 

Some  men  are  brave,  few  men  are  good,  many  men  are  not 
prudent,  are  examples  of  particular  propositions. 

The  quality  of  propositions  we  shall  find  also  to  be  of  two 
kinds — the  quality  of  the  subject-matter  and  the  quality  of  the 
expression.  Propositions  are  divided,  according  to  the  quality 
of  the  subject-matter,  into  true  and  false,  and,  according  to  the 
form  of  expression,  into  affirmative  and  negative. 

It  is  evident  that  with  the  quality  of  the  subject-matter 
Logic  has  directly  nothing  to  do  ;  for,  since  the  logical  form 
of  a  proposition  is  A  is  B,  it  is  taken  for  granted,  as  we  have 
already  seen,  that  this  statement  is  true,  and  that  from  the 
very  form  it  assumes.  With  the  subtleties  of  statements 
Logic  is  not  concerned.  Taking  for  granted  the  truth  of  a 
proposition,  it  makes  use  of  it  properly.  Whatever  falsity 
lies  in  it  will  pervade  the  argument,  but  this  will  not  be  the 
fault  of  Logic.  In  Logic  the  quality  of  the  subject-matter  is 
accidental  and  not  essential. 

The  essential  quality  of  propositions  in  Logic  is,  then,  the 
quality  of  the  expression ;  and  this  quality  is  made,  as  before 
shown,  to  depend  upon  the  copula.  If  the  copula  is  affirmative, 
the  proposition  is  called  affirmative ;  as 

All  A  is  B. 
Some  A  is  B. 

If  the  copula  is  negative,  the  proposition  is  said  to  be  nega- 
tive; as 

No  A  is  B. 

Some  A  is  not  B. 

To  mark  these  divisions  according  to  quantity  and  quality,  and 
to  simplify  the  future  operations  in  which  they  are  used  to 
frame  arguments,  we  employ  letters  as  symbols.  Since  every 
proposition  must  be  universal  or  particular,  and  at  the  same 
time  affirmative  or  negative,  there  are  four,  and  only  four, 
classes  of  simple  categorical  propositions,  which  we  represent 
by  the  following  symbols  : 


QUANTITY    AND    QUALITY    OF    PROPOSITIOxNS.  69 

Universal  affirmative;  as  .1//  A''  ix  i'  by        A. 
Universal  negative;  as  No  X  is  }',  by  E. 

Particular  affirmative;  as  Some  X  /.«  Y,  by     /. 
Particular  negative;  as  Some  Xis  not  Y,  by  0. 

The  sign  of  a  universal  proposition  is  the  same  as  that  of  a 
distributed  term;  i.  e.,  the  prefix  all  or  ev&ry  for  the  universal 
affirmative,  and  no  for  a  universal  negative. 

And  here  it  must  be  particularly  observed  that  the  universal 
negative  is  only  correctly  written  when  in  the  form  no  A  is 
B.  It  might  at  first  sight  seem  that  this  is  equivalent  to  all 
A  is  not  B ;  but  it  is  not  so,  although  often  meant  to  be  so ; 
thus,  all  soldiers  are  not  cruel  has  a  very  difierent  meaning 
from  no  soldiers  are  cruel.  The  first  is  not,  indeed,  a  universal 
proposition,  as  it  appears  to  be,  but  a  particular,  implying 
that  some  soldiers  are  cruel,  while  some  are  not. 

The  translators  of  our  English  Bible  have,  in  a  few  in- 
stances, made  use  of  this  form  improperly  to  express  a  uni- 
versal. Thus,  the  Hebrew  text  of  the  Psalms  expresses  with 
regard  to  the  wicked :  "  All  his  thoughts  are  *  there  is  no 
God  ;'  "  while  the  translators  have  it,  "  God  is  not  in  all  his 
thoughts."  The  meaning  of  the  translators  in  this  is  evi- 
dently, "  God  is  not  in  any  of  his  thoughts." 

The  sign  of  a  particular  proposition  is  the  same  as  that  of 
an  undistributed  term,  i.  e.,  the  prefix  some,  few,  several,  many, 
and  like  words,  indicating  a  part  only  of  a  whole,  for  particular 
affirmative  propositions ;  and  the  same  prefix,  with  a  negative 
y)pula,  for  particular  negative. 

But  it  constantly  happens  that  a  proposition  has  no  prefix, 
and  we  are  then  thrown  upon  our  knowledge  of  the  subject- 
mnttfrr  oi  the  proposition,  to  determine  whether  it  be  universal 
or  particular.  Such  propositions  as  have  no  prefix  to  denote 
their  quantity  are  called  indefinite  propositions,  which  Logic 
alone  will  not  enable  us  to  understand.  We  must  then  look 
to  their  meaning,  and  thus  find  out  what  prefix  is  their  dua 
For  example,  men,  are  arti.^is. 


70 


LOGIC. 


By  examiniug  the  matter  of  this,  we  fiud  that  only  some 
men  are  artists,  and  then,  making  the  proper  prefix,  we  declare 
^he  proposition  to  be  particular. 

Birds  fly.  This  is  true  of  birds  universally,  and  we  have 
the  right  to  prefix  the  sign  all,  which  denotes  it  a  universal 
proposition. 

A  Singular  proposition  is  one  which  has  for  its  subject  a 
singular  term ;  as 

Alexander  was  a  conqueror. 
Caesar  was  ambitious. 

It  would  seem,  at  a  first  consideration  of  the  quantity  of 
these  propositions,  that  they  were  particular,  but  this  is  erro- 
neous ;  they  are  evidently  universal ;  since  when  I  assert  that 
Alexander  was  a  conqueror,  I  mean  the  whole  of  Alexander,  or 
Alexander  taken  in  his  fullest  extension. 

As  a  general  rule,  then,  singular  propositions  are  universal. 
There  are  many  other  divisions  of  propositions  which  are 
curious  rather  than  useful  distinctions.  The  above  are  all 
those  necessary  to  a  comprehension  of  the  logical  processes 
which  follow. 


(29.)  Of  the  Distribution  of  Terms  in  Propositions. 

Having  treated  of  the  quantity  and  quality  of  propositions, 
and  observing  that,  as  we  have  already  seen,  these  proposi- 
tions are  to  be  hereafter  used  in  the  framing  of  syllogisms,  we 
come  to  consider  the  distribution  of  terms  in  propositions,  and 
to  establish  rules  for  this  distribution.  If  we  examine  the  four 
f^ategorical  propositions,  with  their  geometrical  notations — 

A.  J  All  X  is  Y.  ^       ^.  /  No  X  is  Y. 

J.  1  Some  X  is  Y.  ^^^^'  0.  \  Some  X  is  not  Y. 


Aflirm. 


Qrst  with  reference  to  their  subjects,  it  will  be  evident  that  in 


OF  THE  DISTRIBUTION  OF  TERMS  IN  PROPOSITIONS.       71 

A  and  E  the  whole  of  the  subject  being  considered,  the  sub- 
ject is  distributed,  as  is  also  indicated  by  the  prefixes  All  and 
No.  It  will  be  equally  evident  that  in  /  and  0  the  subject  is 
undistributed,  a  portion  only  being  taken,  as  is  indicated  by 
the  prefix  Some. 

The  rule  deduced  then,  as  far  as  the  subjects  are  concerned, 
IS  very  simple ;  it  is,  that 

All  universal  propositions  distribute  the  subject.  No  particu- 
lars distribute  the  subject. 

But  since  the  predicates  in  these  propositions  have  no  such 
prefixes,  how  are  we  to  determine  whether  they  are  distributed 
or  undistributed  ?  By  an  examination  of  the  relation  exist- 
ing between  the  subject  and  predicate  in  each  case,  we  shall 
see  that  the  distribution  of  the  subject  by  no  means  implies 
that  of  the  predicate. 

If  we  assert,  1st,  that  All  X  is  F,  we  do  not  assert  that 
other  things  likewise  may  not  be  contained  in  Y ;  for  though 
All  X  is  F,  All  W  may  be  Y;  All  Z  rtuiy  be  Y,  etc. ;  or,  to 
illustrate  by  a  geometrical  figure,  we  have 


showing  space  enough  for  other  things  besides  X  to  be  contained 
in  Y.  Hence,  it  is  evident  that  the  whole  of  Y  is  not  cou- 
Bidered  in  the  proposition  all  X  is  Y,  or  that  Y.  the  predicate 
is  not  distributed  in  a  universal  aflfirmative  proposition. 

Again,  if  we  take  the  proposition  some  X  is  Y,  the  same 
reasoning  will  apply,  since  many  other  things  may  be  Y,  be- 
sides this  some  X;  as  illustrated  in  the  figure 


72 


LOGIC. 


Likewise  then  we  see  that  the  whole  of  Y  is  not  taken  in 
this  case,  or  that  the  predicate  of  a  particular  affirmative 
proposition  is  not  distributed. 

Thus  far,  then,  we  have  found  it  true  of  affirmative  propo- 
sitions, whether  they  be  universal  or  particular,  that  they  d:  lot 
distribute  the  predicate. 

If,  now,  we  consider  the  universal  negative,  no  X  is  Y,  we 
3 hall  find  that  we  must  consider  the  whole  of  X,  and  the  whole 
oj  Yy  before  we  can  assert  that  no  part  of  one  belongs  to  any 
part  of  the  other ;  thus 


We  have  already  seen  that  the  subject  Xis  distributed,  and 
it  thus  appears  that  in  a  universal  negative  proposition  the  pred- 
icate also  is  distributed.  The  whole  of  the  subject  is  brought 
m  contact  with  the  whole  of  the  predicate,  or  we  could  not 
entirely  deny  their  agreement.  It  remains  now  to  consider 
only  the  predicate  of  a  particular  negative,  some  X  is  not  Y. 
The  same  reasoning  applies  here  as  in  the  last  case ;  or  we 
must  know  and  consider  the  whole  of  Y,  before  we  can  assert 
that  no  part  of  it  belongs  to  the  some  X  in  question. 


It  therefore  appears  that  the  predicate  of  a  particular  nega- 
tive proposition  is  distributed. 

If  we  collect  together  these  four  results,  we  shall   thus 
^tablisb  two  rules : 


CX)NVERSI()N.  73 

ylst.  The  subjects  of  universal  propositions,  and  not  of  par- 
ticulars, are  distributed. 

/     2d.  The   predicate  of  negative  propositions,  and  not  ofy 
I  affirmative,  are  distributed. 

Or,  all  universals  distribute  the  subject,  and  all  negatives 
the  predicate. 

It  may  be  well,  for  the  sake  of  convenient  reference,  to 
arrange  the  quantity  and  quality  of  propositions,  and  the  dis- 
tribution of  the  terms,  in  a  tabular  form,  so  that  it  may  be 
referred  to  until  it  be  fixed  in  the  mind  of  the  student. 

Four  Classes  of  Categorical 


Propositions. 

Suliieci. 

Predicate, 

Simple  Form. 

A. 

Universal  aflBrmative. 

Distributed. 

Undistributed. 

Alfx>s  T. 

E. 

UniTersal  negative. 

Distributed. 

Distributed. 

N^<j) 

I. 

Particular  aflBrmative. 

Undistributed. 

Undistributed. 

Some  X  is  Y. 

0. 

Particular  negative. 

Undistributed. 

Distributed. 

Some  X  is  uoI^y) 

There  is  a  logical  process  which  is  passed  upon  propositions 
and  upon  propositions  only,  and  this  process  has  in  view  the 
use  which  we  make  of  propositions  in  the  framing  of  argu- 
ments. It  is  called  Conversion.  We  cannot  convert  a  temij 
nor  is  it  proper  to  speak  technically,  as  some  writers  have 
done,  of  the  conversion  of  arguments. 

(30.)  Conversion. 
Conversion  consists  in  transposing  the  terms  of  a  propo- 
sition in  such  a  manner  as  to  place  the  subject  for  the  predi- 
cate, and  the  predicate  for  the  subject.  Thus,  having  the 
proposition  A  is  B,  we  convert  it  into  B  is  A.  When  no  other 
change  than  this  is  made,  the  conversion  is  called  simple  con- 
rersion ;  but  by  an  examination  of  the  four  forms  of  cate- 
gorical propositions,  it  will  be  evident  that  they  cannot  all  be 
simply  converted,  and  retain  in  the  converted  proposition  or 
converse  the  truth  of  the  original  proposition  or  exposita.  As 
a  simple  example  of  this  :  having  the  proposition 

All  men  are  mortal, 

we  cannot  write  the  converse^ 
7 


74  LOGIC. 

All  mortals  are  men. 
No  other  conversion  is  allowed  in  Logic  than  that  which 
is  called  illative*  or  that  in  which  we  may  infer  the  truth  of 
the  converse  from  the  truth  of  the  exposita. 

To  simplify  this,  let  us  convert  each  of  these  propositions 
in  turn. 

1.  (A.)  All  X  is  Y  ^  All  men  are  mortals. 
It  is  evident,  as  we  have  already  seen,  that  we  cannot  con- 
vert this  proposition  simply,  for  we  cannot  read 

All  Yis  X  ==  All  mortals  are  men, 
since  Y  (or  mortals)  includes  many  other  races  besides  men. 

We,  therefore,  limit  the  quantity  of  the  proposition  from 
universal  to  particular,  so  that  Y,  which  was  undistributed  in 
the  original  'proposition,  may  remain  so  in  the  converse.  Ex- 
pressing, then,  this  non-distribution  of  Y  by  the  prefix  some, 
we  shall  have  as  the  converse 

Some  Y  is  X  =  Some  mortals  are  men. 
From  the  nature  of  the  process,  this  form  of  illative  conver- 
sion is  called  conversion  by  limitation.'\ 

From  this  we  see  that  the  converse  of  a  universal  affirmative 
is  a  particular  affirmative,  or  A  becomes,  when  converted,  I. 
If  we  examine  the  universal  negative, 

2.  (E.)  No  X  is  Y  =  No  men  are  trees, 
we  shall  see  that  as  X  and  Y  are  taken  in  their  whole  exten- 
sion, or  are  distributed,  we  may  here  convert  simp)ly,  and  read 
No  Y  is  X  =  No  trees  are  men. 
The  converse  of  a  universal  negative  is  a  universal  negative 
S\  likewise,  in  the  particular  affirmative, 

3.  (I.)  Some  X is  Y  ^=  Some  men  are  cruel, 
we  shall  find  that  neither  subject  nor  predicate  is  taken  in  its 

*  In  and  fero  {latum). 

t  The  Latin  name  employed  by  logicians,  for  this  kind  of  conver 
won,  is  conversio  per  accidens. 


CONVERSION.  76 

full  extent  or  distributed,  and  that  wu  luay,  therefore,  con- 
vert simply : 

Some  Y  is  X  =  Some  cruel  {beings)  are  men. 

The  converse  of  a  particular  affirmative  remains  a  particular 
affirmative.  There  remains  only  the  particular  negative  to 
be  considered. 

4.  (O)  Some  X  is  not  Y  =  Some  quadrupeds  are  not  horses. 

This  proposition  presents  a  special  difficulty.  We  cannot 
convert  it  simply  as  in  the  cases  of  E  and  I ;  for  we  should 
then  have  X,  which  is  undistributed  in  the  exposita,  distributed 
in  the  converse ;  thus  we  would  have  the  absurdity 

Some  Y  is  not  X  =  Some  horses  are  not  quadrupeds. 

Nor  can  we  invert  the  process  of  conversion  by  limitation  as 
in  the  case  of  A  (1),  and  pass  back  from  particular  to  uni- 
versal, as 

All  Y  is  not  X  =  All  horses  are  not  quadrupeds. 

To  overcome  this  difficulty  we  detach  the  negaiix^^j^^le 
not  in  the  original  proposition  from  the  copula,  and  attach  it 
to  the  predicate ;  thus,  instead  of  the  usual  form  some  X  is 
not  Y,  we  read, 

Some  X  is  (not  Y)  =  Some  quadrupeds  are  {not  horses), 

and  then  it  is  evident  that  for  all  logical  purposes,  the  propo- 
sition ceases  to  be  0  or  particular  negative,  and  becomes  1  or 
particular  affirmative,  since  for  (not  Y)  we  might  place  any 
other  symbol,  as  Z,  and  convert  by  simple  conversion.  But 
without  this  trouble,  if  we  convert,  we  shall  have 

Some  {not  Y)  is  X  =  Some  {not  horses)  are  quadrupeds, 

or,  in  our  ordinary  language,  to  complete  the  sense, 

Some  {beings  which  are)  not  horses  are  quadrupeds. 

This  is  called  conversion  by  contraposition  or  by  negation. 
We  arrive  by  this  process  at  a  rule  for  illative  conversion. 


76  LOGIC. 

which  is  that  No  term  must  be  distributed  in  the  converse  which 
was  undistributed  in  the  exposita. 

By  arranging  the  different  kinds  of  illative  conversion  in 
tabular  form,  we  shall  simplify  them  for  reference.  Taking 
the  letter  p  to  indicate  conversion  by  limitation  or  per  acci- 
deiu ;  s,  simple  conversion ;  and  k,  conversion  by  negation,  we 
shall  have  the  following  table : 

ILLATIVE  CONVERSION. 

Original  Propositions.      Methods  of  Converting.       Converted  Propositions. 

(A)  All  X  is  Y.  p.  Some  Y  is  X.  (I.) 

(E)  No  X  is  Y.  s.  No  Y  is  X.  (E.) 

(I)  Some  X  is  Y.  s.  Some  Y  is  X.  (I.) 

(O)  Some  X  is  not  Y.  k.  Some  (not  Y)  is  X.  ( L) 

The  above  are  the  regular  forms  of  conversion,  but  there  are 
certain  Additional  conversions  to  be  noticed.  It  must  be 
remarked  that  the  universal  affirmative, 

All  X  ^s  F  =  All  men  are  mortals, 

is  sometimes  converted  in  another  manner ;  i.  e.,  by  putting 
immediately  before  both  subject  and  predicate  the  negative 
particle  not,  and  then  converting  ;  thus, 

All  (not)  Yis  {not)  X  =  All  (not)  mortals  are  {not)  men; 

i.  e.f  All  (who  are  not)  mortals  are  not  men;  or,  in  common 
phrase.  None  but  Y  can  be  X  =  none  but  mortals  can  be  men. 
Again  (E),  which  is  converted  simply,  may  be  likewise 
converted  by  limitation,  since,  if  having  the  universal  form, 

No  A  is  B  =  No  men  are  trees, 
we  c-an  say 

No  B  is  A  =  No  trees  are  men, 

we  can  also  «ay,  what  is  less  than  this, 

Some  B  is  not  A  =  Some  trees  are  not  men. 

It  may  happen  that  for  some  purpose  of  logical  technical- 
ity it  will  be  better  to  use  the  particular  when  we  have  a 
right  to  use  the  universal,  but  from    the  existence  of  the 


CONVERSION.  77 

universal  wt    iul'er   that  of  the  particular,  which   is  only  a 
part  of  it. 

There  remains  only  one  remark  to  be  made  upon  the  subject 
of  conversion ;  it  is  that  there  are  a  few  propositions  whicli 
bear  the  form  of  A  or  universal  affirmative,  which  are  cipabk' 
of  simple  conversion.  The  terms  of  such  a  proposition  are 
said  to  be  convertible  terms,  or  the  predicate  and  subject  are 
either  exactly  equivalent  or  exactly  co-extensive ;  for  example, 
in  the  proposition  All  common  salt  is  chloride  of  sodium,  we 
have  a  right  to  assert  that  all  chloride  of  sodium  is  common 
salt.  From  the  proposition  All  the  good  are  saved,  we  have  a 
right  to  infer  that  All  (who  are)  saved  are  good.  ^LsLuy  just 
definitions  come  under  this  class.  Besides  such  propositions 
as  these,  there  are  many  mathematical  propositions  which 
seem  to  be  single  propositions  with  convertible  terms,  when 
in  reality  they  contain  two  distinct  propositions,  each  of 
which  requires  distinct  proof.  Thus,  All  equilateral  triangles 
are  equi-angular.  The  apparent  converse  that  All  equi-angu- 
lar  triangulars  are  equilateral,  is  indeed  true,  but  this  is  not 
inferred  from  the  original  proposition  ;  it  is  proved  separately 
by  geometricians ;  so  that,  instead  of  being  the  converse  of 
the  proposition  stated,  it  is,  in  reality,  a  distinct  proposition. 

The  processes  of  conversion  have  been  applied  above  only 
to  the  forms  of  simple  categorical  propositions ;  they  may  like- 
wise be  applied,  however,  to  compound  propositions,  and,  when 
we  come  to  consider  these,  we  shall  show  how  they  may  be 
converted  ;  but  it  may  be  here  observed,  that  as  all  compound 
propositions  may  be  readily  reduced  to  the  simple  categorical 
form,  having  shown  how  to  convert  these,  we  have  in  reality 
shown  how  to  convert  them  all. 

The  next  process  of  importance  in  considering  propositions 
is  the  manner  and  character  of  their  opposition  to  each  other, 
and  this,  like  the  process  of  conversion,  becomes  of  special 
value  when  we  are  joininic  propositions  together  to  frame 
arguments. 


78  LOGIC. 

(31.)  Of  Opposition. 
Two  propositions  are  said  to  be  opposed  to  each  othei 
when,  having  the  same  subject  and  predicate,  the  one  denie* 
tithe''  entirely  or  in  part  what  the  other  affirms,  or  affirtns  either 
entirely  or  in  part  what  the  other  denies ;  as,  for  instance,  tlio 
proposition 

,.,    .„  .  ,.  J  1     1    i.1    \  yo  nun  are  mortal.  (E.) 

(A)  .1//  mm  are  mortal  is  opposed  by  both  |  ^,.,^,^^^.  ,^^^,^  ^,,.^  ,^^^^  ,,,^^,.^^,^  ^^^^j 

J  /,,,x  ,r  I  •  1  1     1    »u  ^  All  anqds  are  men.  (A.) 

and  (L)  No  angels  are  mm  is  opposod  by  both  |  ^^,,„^  ^!^^g^^  ^^,,.^  ,„^,,         f  j  j 

Again,  two  propositions  are  said  to  be  opposed  when,  hav- 
ing the  same  subject  and.  predicate,  the  one  affirms  in  ivhole  what 
the  oth&t'  affirms  in  part,  or  denies  in  whole  what  the  other  denies 
in  part;  thus, 

(A)  All  men  are  mortal.      {0pp.)      Some  men  are  mortal.       ( I.) 
(E)  No  men  are  trees.  [Opp.)      Some  men  are  not  trees.  (O.) 

Or,  the  rule  may  be  more  concisely  stated  thus :  two  propo- 
sitions are  said  to  be  opposed  to  each  other  when,  having 
the  same  subject  and  predicate,  they  differ  in  quantity  or  in 
quality,  or  in  both. 

It  will  appear,  then,  that  the  opposition  in  propositions  is 
both  in  quantity  and  in  quality,  and  as  there  are  four  forms 
of  categorical  j^ropositions,  and  any  two  may  be  thus  op- 
posed, we  shall  have  four  kinds  of  opposition,  which  will  best 
be  illustrated  by  the  following  figure  : 


^   N  T 

contraries 

FN    E 

I  F 

T  I 

0  F 

as 

F  C 

C 

c 

T  3 

1      00 

O 
balterns 

N  T 

sub-contraries 

F  N 

I  F 

T  I 

C  T 

T  C 

In  which  the  two  universal  propositions  A  and  E  are  called 
contraries  and  differ  only  in  quality,  being  respectively  affirm- 


OF    THE    MAFIER    OF    PROPOSITIONS.  79 

cUive  and  negative;  the  two  particulars  I  and  O  are  called 
sub-corUraries,  differing  likewise  in  quality  only ;  the  two 
affirmatives  and  the  two  negatives  are  called  respectively  sub- 
alterns, differing  in  quantity  only ;  the  universal  affirmative 
and  particular  negative,  and  the  universal  negative  and  par- 
ticulur  affirmative,  are  respectively  called  contradictcries,  and 
differ  both  in  quantity  and  quality. 

If  we  desire,  as  in  applying  Logic  we  may  do,  to  determine 
the  relative  truth  and  falsity  of  these  respective  propositions, 
we  must  look  for  a  moment  at  the  matter  which  they  may 
contain. 

(32.^  Of  the  Matter  of  Propositions. 

The  matter  of  a  proposition  is  the  nature  of  the  connection 
between  the  terms  of  the  proposition,  or,  in  ordinary  language, 
the  exaxi  meaning  of  the  proposition. 

By  considering  the  nature  of  this  connection  between  the 
terms,  we  shall  see  that  it  can  be  of  only  three  kinds :  neces- 
mry,  which  is  expressed  by  an  affirmative  proposition ;  im- 
possible,  expressed  by  a  negative  proposition,  and  contingent, 
which  is  expressed  by  a  particular  proposition. 

To  illustrate :  if  we  have  given  to  us  the  two  terms,  men 

and  mortal,  and  are  told  to  connect  them  by  a  copula,  we  ask 

ourselves,  what  is  the  nature  of  the  connection  between  these 

two  ?     The   answer  is,  it  is   necessary,   and  we  express   that 

necessity  by  using  an  affirmative  copula,  and  prefixing  the 

«ign  All: 

All  men  are  mortal. 

Again,  if  we  have  given  to  us  the  two  terms  men  and  trees, 
to  perform  an  analogous  operation,  we  shall  assert  the  nature 
of  the  connection  between  them  to  be  impossible,  and  express 
that  impossibility  by  the  use  of  the  prefix  No — 

No  men  are  trees. 
If,  again,  we  have  the  terms  men  and  handsome,  we  assert  the 
pp**Are  of  the  connection  to  be  contingent,  as  some  men  arf 


80  LOGIC. 

and  some  are  not  handsome;  and  thus  to  express  contingem 
matter  we  write  the  proposition  with  the  prefix  some : 

Some  men  are  handsome. 
Some  men  are  not  handsome. 

If,  now,  we  examine  the  matter  of  these  propositions  we  shall 

see  that, 

In  necessary  matter,  all  affirmatives  are  U^ue  and  negatives 

false. 

Necessary  Matter. 
True.  False. 

(A)  All  men  are  mortal.  (E)  No  men  are  mortal. 

(I)    Some  men  are  mortal.  (O)  Some  men  are  not  mortal. 

In  impossible  matter  all  negatives  are  true  and  affirmative^: 

false. 

Impossible  Matter. 
True.  False.     . 

(E)  No  men  are  trees.  (A)  All  men  are  trees. 

(0)  Some  men  are  not  trees.  (I)    Some  men  are  trees. 

In  contingent  matter  all  particulars  are  true  and  universale 

false. 

Contingent  Matter. 
True.  False. 

(1)  Some  men  are  handsome.  (A)  All  men  are  handsome. 
(O)  Some  men  are  not  handsome,         (E)  No  men  are  handsome. 

From  this  examination  we  perceive  that  if  one  contrary  is 
true  the  other  must  be  false,  but  if  one  is  false  the  other  may  be 
false  also ;  if  one  sub-contrary  is  false  the  other  must  be  true, 
but  if  one  is  true  the  other  may  be  true  also.  But  in  the  case 
of  contradictories,  if  one  is  either  true  or  false,  the  other  must 
be  just  the  opposite,  i.  e,,  false  or  trus. 

It  remains  to  consider  the  subalterns,  which  differ  in  quan- 
tity. If  the  universal  (A  or  E)  be  true,  the  particular  (I  oi 
0)  will  be  true  also  ;  as 

(A)  All  men  are  mortal,  (E)  No  men  are  trees, 

implies  implies 

^  I)    Some  men  are  mortal.  (O)  Some  men  are  not  trees. 


OP   COMPOUND    PROPOSITIONS.  81 

If  the  particular  I  or  O  be  true,  the  universal  A  or  E  i:i 
not  necessarily  true. 

(I)  Some  islands  are  fertile  does  not  permit  us  to  infer  (A) 
All  islands  are  fertile. 

(O)  Some  islands  are  not  fertile  does  not  permit  us  to  imply 
(E)  JVb  islands  are  fertile. 

But  if  the  particular  he  false,  the  universal  must  of  necessity 
bfc  false  also.  Thus,  the  false  particular  Some  men  are  trees 
would  give  us  also  All  men  are  trees  as  a  false  universal. 

By  summing  up  these  inferences  we  may  state  the  following 
rules,  which  must  be  kept  in  the  memory  as  we  approach  the 
subject  of  Reduction. 

I.  Contraries  may  both  be  false,  but  never  both  be  trus. 

II.  Sub-contraries  may  both  be  true,  but  never  both  false. 

III.  Of  ContradictoHes,  if  one  be  false  the  other  must  be 
true,  and  vice  versa. 

IV.  In  Subalterns  we  reason  from  the  affirmation  only  of  the 
universal  to  the  affirmation  of  the  particular ;  but  from  the 
denial  of  the  particular  to  the  denial  of  the  universal. 

The  letters  N  I  C  at  the  corners  of  the  figure  indicate 
necessary,  impossible  and  contingent  matter ;  T  means  true,  and 
F  false. 

The  passage  from  one  proposition  to  another  in  conversion 
and  opposition  is  called  by  some  writers  immediate  inference. 

With  the  remark  that  opposition  may  be  also  illustrated 
in  compound  propositions,  or  those  not  directly  in  the  simple 
categorical  form,  or  that  such  propositions  may  be  reduced  to 
this  simple  form  by  an  easy  process  still  to  be  explained,  we 
pass  to  the  subject  of  compound  propositions. 

(33.)  Of  Conipound  Propositions. 
A  compound  proposition  consists  of  two  or  more  simple 
propositions,  united  together  either  by  a   simple  copulate, 
expressed  or  understood,  or  by  a  conjunction  denoting  an 
hypothesis. 

F 


S2  LOGIC. 

Compound  propositions  are  consequently  divided  into  two 
classes,  categorical  and  hypothetical. 

Compound  categorical  propositions  are  of  two  kinds,  copuMivt 
and  discretive. 

A  copulative  proposition  consists  of  two  or  more  subject* 
united  with  the  same  predicate,  or  with  two  or  more  predi 
cates,  by  the  use  of  the  copulative  conjunction ;  as, 

Men,  horses  and  birds  are  animals. 

A  discretive  proposition  consists  of  two  simple  propositions, 
which  are  contrasted  on  account  of  an  apparent  inconsistency , 

as. 

Fox,  though  dissolute,  was  a  patriot. 

In  this  a  third  proposition  is  implied,  viz.,  the  general  in- 
congruity of  patriotism  with  dissoluteness. 

Many  compound  propositions  are  tacit  or  implied,  and  thus 
have  the  form  of  simple  propositions. 

A  hypothetical  proposition  consists  of  two  or  more  simple 
propositions  united  by  a  conjunction  which  expresses  hypoth- 
esis. This  conjunction  is  usually  placed  at  the  beginning  of 
the  proposition. 

Hypothetical  are  divided  into  conditional,  di^unctive  and 
causal,  and  take  these  names  from  the  conjunctions  which 
express  the  condition  of  the  hypothesis. 

A  conditional  proposition  expresses  the  condition  by  the 
conjunction  if;  as, 

If  A  is  B,  C  is  D  =  If  John  return,  Harry  will  go. 

A  disjunctive  proposition  is  formed  with  the  conjunctions 
either  and  or;  as. 

Either  A  is  B,  or  C  is  D  =  Either  John  is  wrong,  or  James  is  ill. 

A  causal  proposition  unites  its  parts  by  the  conjunction 

because ;  as, 

A  is  B  because  C  is  D. 
John  is  well  because  he  is  prudent. 


OF   COMr>C)UND    PROPOSITIONS.  83 

It  is  evident,  in  the  case  of  categorical  propositions,  thai 
they  may  be  at  once  resolved  into  the  simple  {)ropositions  of 
which  they  are  composed  :  thus  we  may  divide  the  copulativt 
proposition  given  into  three  distinct  propositions,  viz., 

Men  are  animals, 
Horses  are  animals, 
Birds  are  animals. 

and  the  discretive  may  be  divided  into  two,  thus : 

Fox  was  dissolute. 
Fox  was  a  patriot. 

Unlike  the  compound  categorical  propositions,  the  hypo- 

theticals  contain  within  themselves  the  germ  of  an  argument, 

and  only  require  that  the  hypothesis  shall  he  established,  or  fail 

of  establishment,  to  arrive  at  a  conclusion.     Thus,  having  the 

proposition, 

If  A  is  B,  C  is  D, 

we  need  only  know  whether  A  is  B,  in  order  to  state  the 
argument  and  arrive  at  the  conclusion  that  C  is  D. 

Conditional  propositions,  however,  may  be,  in  every  case, 
reduced  to  a  categorical  form,  by  regarding  them  as  universal 
affirmative  categorical  propositions,  of  which  the  antecedent  is 
the  subject,  and  the  consequent  the  predicate.  We  then  rid 
ourselves  of  the  condition,  by  the  use  of  the  words  "  the  case 
of;"  thus,  instead  of  the  form,  If  A  is  B,  C  is  D,  we  shall 
have 

( The  case  of)  A  being  B,  is  {the  case  of)  C  being  D, 

which  is  purely  categorical  in  form. 

Disjunctive  propositions  may  be  reduced  to  conditionals; 
thus: 

Either  A  is  B,  or  C  is  D,  is  equivalent  to  if  A  is  not  B,  C  is  D, 

or  we  may  place  it  at  once  in  a  categorical  form  without  this 
double  process,  by  reading  it  thus : 

The  txjDO  possible  cases  in  this  matter  are  tha   A  is  B,  and  that  C  is  D. 

It  is  more  usual  to  reduce  the  disjunctive,  however,  to  a 
conditional  form,  into  wnich  it  very  naturally  fjilLs. 


84  LOGIC. 

The  caiisal  proposition, 

Because  A  is  B,  C  is  D, 
becomes  either  at  once  categorical,  when  we  establish  the 
truth  of  because,  and  thus  we  have 

A  is  B,  therefore  C  is  D, 
as  an  enthymeme,  to  which,  having  the  subject-matter,  we 
might  supply  the  wanting  premiss ;  or  the  causal  proposition 
becomes  simply  conditional,  if  the  cause — expressed  by  the 
first  proposition  A  is  B — be  doubtful,  and  then  we  read, 

If  A  is  B,  CisDy 

which  must  be  treated  like  the  conditional  above. 

As  it  seems,  then,  that  all  these  are  reducible  to  the  con- 
ditional form,  we  need  only  show  how  the  process  of  conver- 
sion is  applied  to  conditionals,  in  order  virtually  to  apply  it  to 
them  all.  From  what  has  been  said,  it  will  appear  that  con- 
ditionals are  converted  by  negation  only ;  thus,  to  convert  the 
proposition, 

If  John  has  the  smallpox  he  is  sick, 

we  may  read — 

If  John  is  not  sick  he  has  not  the  smallpox ; 

or,  the  conversion  rests  upon  the  fact  that  the  denial  of  tht 
consequent  leads  to  the  denial  of  the  antecedent. 

We  cannot  convert  without  this  negation,  for  we  could  not 
reason  from  the  affirmation  of  the  consequent  to  the  affirmation 
of  the  antecedent;  thus, 

If  John  is  sick  he  has  the  smallpox, 

aince  that  consequent  (sickness)  may  have  sprung  from  some 
other  antecedent  than  the  smallpox. 

(34.)  The  New  Analjrbic. 
And  here  it  becomes  necessary,  before  closing  the  subject 
of  proportions,  to  refer  briefly  to  the  effort  of  certain  late 
writers  to  quantiftj  the  predicate;   that  is,  to  place  prefixe? 


THE    NfeW    ANALYTIC.  85 

before  it  similar  to  those  placed  before  the  subjects  of  propo- 
sitions to  determine  at  a  glance  its  distribution  or  non-distri- 
bution, and  to  form  thus  a  new  set  or  class  of  categorical 
propositions.  Thus,  instead  of  the  form  all  men  are  animah^ 
they  would  write  all  men  are  some  animals,  and  claim  thereby 
not  only  a  greater  precision  in  the  logical  statement,  but  in 
some  instances  the  establishment  of  a  distinct  proposition  ;  a.«s 
for  example, 

All  A  is  (all)  B. 

It  may  be  admitted  that  sometimes  a  new  idea  is  suggested 
by  such  a  quantification  of  the  predicate,  but  it  is  only  sug- 
gegted,  not  contained  in  the  proposition  thus  rendered.  Thus, 
if  we  say, 

All  men  are  sinners, 

we  mean  by  (jur  rule,  some  sinners;  now  the  question  as  to 
the  comprehension  of  this  word  sinners  may  arise,  when  we 
place  such  a  prefix ;  whether  angels  and  devils  may  or  may 
not  be  included  in  it ;  and  whether  the  ill-conduct  of  brutes 
is  excluded  from  it.     Whereas,  if  we  could  write. 

All  men  are  (allj  sinners, 

we  should  exclude  at  once  all  other  beings  from  the  category. 
Hence,  the  quantification  of  the  predicate,  which  in  the  old 
system  is  implied,  does,  when  expressed,  suggest  new  thoughts 
or  judgments,  but  those  new  judgments  rest  upon  their  own 
basis,  and  have  really  nothing  to  do  with  the  original  propo- 
sition. There  seems  really,  therefore,  nothing  gained  in  the 
extension  of  the  proposition  by  this  attempt  to  quantify  the 
predicate,  but  rather  a  confusion  of  judgment  and  a  compli- 
cation of  logical  forms. 

It  is  not  intended  to  give,  in  detail,  the  applications  of  the 
"new  analytic,"  nor  to  deny  that  results,  totally  out  of  the 
province  of  Logic,  are  attained  by  it.  It  is  evident  that  'f 
we  quantify  the  predicate,  in  categorical  propositions,  we  shalJ 
have  four  additional  forms,  viz. : 

H 


86 

Established  Forms. 

A. 

All  A  is  B. 

£. 

No  A  is  B. 

I. 

Some  A  is  B. 

0. 

Some  A  is  not  B. 

LOGIC. 


Xew  Forms. 

All  A  is  all  B. 

X. 

No  A  is  some  B. 

y. 

Some  A  is  all  B. 

u. 

Some  A.  is  not  some  B. 

z. 

Now  of  these  new  forms  we  have  already  considered  X,  as  'r* 

the  case, 

All  equilateral  triangles  are  {all)  equi-angular, 

and  in  the  cases  of  exact  definitions,  as 

All  common  salt  is  (all)  chloride  of  sodium. 
In  the  first  we  have  seen  that  there  are  hvo  distinct  proposi- 
tions, and  in  the  second  that  there  are  but  two  names  for  the 
same  object. 

As  for  Y,  U  and  Z,  they  are  so  clearly  contained  in  the 
old  forms  that  they  need  but  little  elucidation. 

U.         Some  trees  are  all  oaks, 
when  converted  gives  us 

All  oaks  are  trees,  or  A. 

Y.  No  heroes  are  some  men. 

Conv.     Some  men  are  not  heroes.  O. 

Z.  Some  quadrupeds  are  not  some  horses. 

By  which  we  determine  that  the  quadrupeds  referred  to  may 
belong  to  other  species,  or  may  be  included  in  the  species 
horse,  apart  from  the  some  horses  mentioned. 


It  was  attempted,  in  the  new  analytic,  to  simplify  the  subject 
of  conversion,  but,  it  seems,  with  inadequate  results. 

And  here  we  leave  the  subject  of  quantifying  the  predicate, 
80  far  as  it  relates  to  propositions  alone.  If  carried  out  in  the 
syllogism,  it  would  much  enlarge  the  domain  of  Figure,  and 
give  much  fruitless  labor  to  the  logician. 


CHAPTER    VII. 

(35.)  Of  Argnments. 

Am  argumeni  is  an  act  of  reasoning  or  'i  atiodnation.  It 
consists  of  two  parts  :  that  to  be  proven,  and  that  by  which 
it  is  proven. 

The  part  to  be  proven  is  embodied  in  the  conclusion,  and 
that  by  which  it  is  proven  is  embodied  in  the  premisses. 
When  these  are  inverted  from  the  usual  logical  order,  so  that 
the  conclusion  is  stated  first,  it  is  called  the  question;  and  the 
premisses  which  are  joined  to  it  by  the  word  because,  are  then 
called  the  reason ;  thus, 

(Question)    Why  are  all  Americans  mortal  f 
or    All  Americans  are  mortal, 
Because    They  are  men. 

But  in  logical  form  and  order  the  premisses  are  stated  first, 
and  the  conclusion  is  connected  with  them  by  the  illative 
conjunction  therefore;  thus, 

r 

[A 
Therefore       All  Americans  are  mortal. 

These  two  forms  must  be  distinguished  from  what  is  expressed 
by  the  words  inference  and  proof,  which  have  not  to  do  with 
the  order  of  the  parts  in  an  argument,  but  with  the  special 
design  of  the  person  who  uses  the  argument;  i.  e.,  whether 
from  known  facts  or  premisses,  he  seeks  to  establish  a  conclu- 
sion ;  01  has  adopted  a  conclusion,  and  is  simply  seeking  for 
premisses  by  which  to  substantiate  it. 

Logic  teaches  us  to  draw  from  Ruown  proofs  only  a  just 
inference,  or  ^-^  maintain  n  c^iven  inference  ou\\  h\  jud  proofs 

87 


_        .  ,  All  men  are  mortal. 

Premisses    i   .  „    . 

All  Americans  are  men. 


88  LOGIC. 

We  may  more  clearly  illustrate  by  observing  how,  iu  tti« 
various  professions,  these  different  methods  are  used ;  thus,  a 
naturalist  gets  together  many  observations  and  makes  many 
experiments,  forming  a  strong  store  of  proofs,  before  he  may 
justly  iiifer  a  conclusion,  while  an  advocate  at  law  assumes 
the  innocence  of  his  client  or  the  guilt  of  the  prisoner,  as  a 
foregone  conclusion,  and  then  uses  every  means  for  obtaining 
proofs  and  thus  establishing  premisses  by  which  to  substantiate 
his  conclusion. 

It  has  been  observed  that  the  logical  form  of  an  argument 
is  a  syllogism,  which  consists  of  three  propositions ;  i.  e.,  two 
premisses  and  a  conclusion. 

After  fully  explaining  the  syllogism,  we  shall  consider  all 
forms  of  irregular  and  abridged  arguments,  and  show,  as  has 
been  asserted,  that  they  may  all  be  reduced  to  this  simple 
form,  so  that  the  logical  tests  may  be  at  once  applied  to  them. 

(36.)  Of  the  Syllogism. 
In  the  analysis  of  Logic,  the  dictum  of  Aristotle  was  dis- 
tinctly laid  down  and  illustrated.     Its  form  was : 
No.  1.  No.  2. 

All  A  is  B.  No  A  is  B. 

All  or  some  C  Is  A.  All  or  some  C  is  A. 

All  or  some  C  is  B.  No  C  is  B,  or  some  C  is  not  B. 

The  principle  of  the  dictum  is,  that  whatever  (B)  we  pred- 
icate (in  the  major  premiss)  of  the  whole  class  (All  A) ;  under 
which  class  we  assert  (m  the  minor  premiss)  certain  individ- 
uals (All  or  some  C)  to  be  ranged ;  we  may  also  predicate 
(in  the  conclusion)  of  those  individuals. 

Thus,  B  is  predicated  of  (All  A),  C  is  an  individual  of 
the  class  A,  therefore  we  have  a  right  to  predicate  B  of  C. 

But,  as  few  arguments,  in  the  ordinary  uses  of  language, 
are  placed  in  this  exact  form  (although  all  valid  arguments 
may  be),  there  have  been  laid  down  two  logical  axioms  and 
several  important  rules  for  determining  the  validity  of  syllo 
gisms  without  the  labor  of  brinsring  them  to  this  form. 


LOGICAL    AXIOMS.  89 

It  must  be  constantly  remembered  that  it  is  a  conditiun  of 
every  syllogism  that  it  contains  three  and  only  three  terms : 
the  major  term,  the  minor  term,  and  the  middle  term.  The 
first  two  of  these  terms  must  not  be  confounded  with  the 
premisses  which  bear  the  same  name,  and  which  are  proposU 
tiotis.     Thus  in  the  example : 

mid.  maj.  mid.  maj 

Maj.  prem.     A     is     B    =     All  men  are  mortal. 
min.  mid.  minor.  mid. 

Min.  prem.    C     is    A    =    All  Americans  are  men. 

min.  m/jj.  minor.  major. 

Concl.  C     is    B    =     All  Americans  are  mortal. 

B  is  the  major  term,  and  it  is  in  the  major  premiss ;  C  is  the 
minor  term,  and  it  is  found  in  the  minor  premiss ;  A  is  the 
middle  term,  because  it  is  the  medium  of  comparison  between 
the  other  two.  In  the  major  premiss,  the  middle  term  is  com- 
pared with  the  major ;  in  the  minor  premiss  it  is  compared 
with  the  minor,  and  in  the  conclusion,  the  minor  and  major 
terms,  having  been  thus  found  to  agree  with  the  same  middle 
term,  are  asserted  to  agree  with  each  other. 

The  minor  term  is  always  the  subject  of  the  conclusion,  and 
the  major  term  the  predicate. 

This  simple  process  of  comparison  leads  us  to  the  statement 
of  those  axioms  which  determine  the  conditions  of  agree- 
ment and  disagreement  between  the  major  and  minor  terms, 
and  to  note  some  important  consequences  following  from  them. 

(37.)  Logical  Axioms. 

1st.  If  two  terms  agree  with  one  and  the  same  third  term, 
they  will  agree  with  each  other. 

2d.  If  of  two  terms,  the  one  agree  and  the  other  iisagree 
with  one  and  the  same  third  term,  they  will  disagree  with 
each  other. 

Rules. 

I.  From  the  first  of  these  axioms  we  observe  that  if  both 
premisses  of  a  syllogism  are  affirmative,  thus  expressing  the 

8* 


90  LOGIC. 

agreement  of  the  major  and  minor  terms  with  the  middle,  the 
conclusion  must  likewise  be  affirmative,  or  express  the  agree- 
ment between  these  two  terms;  thus,  B  being  the  major  term, 
C  the  minor,  and  A  the  middle,  we  have 

A  is  (or  agrees  with)  B, 
C  is  (or  agrees  with)  A, 

and  we  must  consequently  state  the  conclusion 

C  is  (or  agrees  with)  B. 

II.  Again,  from  the  second  axiom,  we  see  that  if  one  of 
the  premisses  {as  the  major)  be  affirmative,  and  thus  express 
the  agreement  between  the  major  term  and  the  middle,  and 
the  other  be  negative  and  thus  express  a  disagreement  between 
the  minor  term  and  the  middle,  we  must  have  a  negative  con- 
clusion to  express  the  disagreement  between  the  major  and 
the  minor,  which  we  have  thus  shown,  the  one  to  agree  and 
the  other  to  disagree  in  the  premisses  with  one  and  the  same 
third  (the  middle). 

Thus,  if  A  is  not  {or  disagrees  ivith)  B, 
And  if  C  is  {or  agrees  with)  A, 
we  must  have,  C  is  not  (or  disagrees  with)  B. 

III.  It  is  further  evident  that  if  both  premisses  be  negative, 
ive  can  draw  no  conclusion;  because  in  these  premisses  the 
middle  term,  simply  disagreeing  with  both  the  major  and 
minor  terms,  is  no  longer  a  medium  of  comparison  between 
them.     For  example,  state  the  premisses. 

No  A  is  B  =  No  men  are  trees. 
No  C  is  A  =  No  horses  are  men ; — 

Wr  have  established  no  relation  whatever  between  C  and  B, 
or  between  horses  and  trees,  so  that,  although  we  might  truth- 
fully write 

No  horses  are  trees, 

it  would  be  an  accidental  statement,  and  not  spring  from  the 
premisses  stated. 

In  the  conclusion  is  stated  the  relation  betiveen  the  majo? 


LOGICAL    AXIOMS.  91 

and  minor  term,  which  wiis  established  in  the  premisses  by 
the  medium  of  the  middle  term.  The  minor  term  is  the  true 
subject  of  the  conclusion,  and  the  major  terra  the  true  predi- 
cate. Sometimes  in  an  inverted  or  elliptical  Cvmclusion  these 
t€rms  may  appear  transposed,  but  when  properly  written  out 
they  will  take  the  places  indicated. 

The  middle  term,  which  occurs  twice  in  the  premisses,  is 
the  medium  of  comparison  between  th6  two  other  terms,  and 
is  generally  the  name  of  a  class,  of  which  in  one  premiss  some- 
thing is  predicated,  or  to  which  some  quality  is  attributed,  as 
1.  Man  is  a  rational  animal, 

in  which  man  is  the  name  of  a  class,  and  rationality  a  predi- 
cate or  attribute :  under  which  in  the  other  premiss  we  range 
an  individual  or  individuals  belonging  to  the  class,  as 

2.  John  is  a  man, 

and  by  means  of  which  we  have  a  right  to  predicate  or  at- 
tribute this  same  thing  rationality  to  the  individual ;  thus, 
3.  John  is  a  rational  animal. 

IV.  Ambiguous  middle. 

It  is  scarcely  necessary  to  state  that  the  middle  term  must 
be  univocal,  i.  e.,  must  have  the  same  meaning  in  both  pre- 
misses. If  it  be  ambiguous,  or  possess  one  meaning  in  the 
major  premiss  and  a  different  one  in  the  minor,  we  shall  vio- 
late the  first  principle  in  the  construction  of  a  syllogism,  and 
have  four  terms  instead  of  the  three,  and  only  three,  required. 
Most  languages  have  many  such  ambiguous  words,  and  the 
English  particularly  is  full  of  them :  thus 

1.  A  bank  is  a  financial  institution. 

2.  The  margin  of  a  stream  is  a  bank. 

3.  The  margin  of  a  stream  is  a  financial  institution. 

Many  such  glaring  examples  will  occur  at  once  to  the  stu- 
dent ;  but  it  must  be  remembered  that  the  sophist  who  would 
construct  his  artful  fallacies  to  deceive,  does  not  employ  such 


92  LOGIC. 

manifestly  ambiguous  words,  but  those  whose  double  meau 
ings  are  much  more  nearly  the  same. 

Thus,  in  their  philosophic  meanings,  the  words  church  and 
faith  have  given  rise  to  sharp  controversy  and  violent  partisan 
ships.     As  ambiguous  terms  play  a  very  prominent  part  in  the 
subject  of  Fallacies,  we  shall  recur  to  them  under  that  head 

When  the  argument  is  written  out  in  symbols,  the  ambi- 
guity either  disappears  entirely,  that  is,  when  we  represent 
the  term  in  both  premisses  by  the  same  letter,  thus, 

^  is  B, 

C  is^, 

C  is  B, 

or  it  becomes  at  once  manifest,  when  we  represent  the  term 
in  the  major  premiss  by  one  symbol,  as  A,  and  that  in  the 
minor,  having  a  different  meaning,  by  another,  as  D,  thus, 

A  is  B, 

C  isD, 

in  which  premisses  there  are  four  terms,  and  the  error  dis- 
tinctly appears. 

V.    Undistributed  middle. 

The  middle  term  must  be  distributed ;  i.  e.,  taken  in  its 
whole  comprehension,  at  least  in  one  of  the  premisses,  for  it 
will  otherwise  occur  that  we  may  compare  the  major  term 
with  one  part  of  the  middle,  and  the  minor  with  another  part, 
and  thus  it  would  fail  to  be  a  just  medium  of  comparison. 
It  might  happen,  by  chance,  that  these  two  parts  should 
be  the  same,  but  it  would  be  only  by  chance;   in  the  gene- 
ral case  they  would  be  different  parts,  and  if  we  choose  to 
regard  each  part  as  a  distinct  term,  we  should  again  run  into 
:he  error  of  having  four  terms  instead  of  three;  thus. 
Some  quadrupeds  are  cows, 
Some  quadrupeds  are  sheep, 
Therefore  Some  sheep  are  cows. 
White  is  a  color, 
Black  is  a  color, 
Therefore   Black  is  white 


LOGICAL    AXIOMS.  93 

But  if  one  of  the  extremes  be  compared  with  the  iv/iole  of 
the  middle  term,  and  the  other  be  compared  only  with  a  part, 
which  part  is  necessarily  contained  in  the  whole,  they  may 
then  be  compared  with  each  other. 

VI.  Illicit  process. 

Again,  in  order  to  distribute  either  the  major  or  minor  term 
in  the  conclusion,  it  must  have  been  previously  distributed  in 
the  premiss  in  which  it  occurs :  because,  we  only  have  a  right 
to  compare  that  part  of  the  term  with  the  other,  in  the  con- 
clusion, which  we  have  already  compared  with  the  middle  in 
the  premiss ;  thus, 

All  men  are  animals, 
No  dogs  are  men. 
Therefore  No  dogs  are  animals. 

The  technical  name  for  this  logical  fallacy  is  the  illicit  prO' 
cess.  In  the  example,  the  major  term,  animals,  which  is  not 
distributed  in  the  premiss  (as  it  is  the  predicate  of  an  affirm- 
ative proposition)  is  distributed  in  the  conclusion  (as  the  pred- 
icate of  a  negative  proposition) ;  this  is  called  an  illicit  process 
of  the  major  term  ;  if  it  be  the  minor  term  thus  treated,  it  is 
called  an  illicit  process  of  the  minor  term. 

The  following  is  an  example  of  illicit  process  of  the  minor. 

1.  All  men  are  rational  beings, 

2.  All  men  are  animals, 

3.  All  animals  are  rational  beings. 

In  this  example  the  minor  term  animals,  which  is  undistrib- 
uted in  the  minor  premiss — as  the  predicate  of  an  affirmative 
proposition  — is  distributed  in  the  conclusion,  being  there  the 
subject  of  a  universal. 

Let  it  be  remembered  that  this  is  called  an  illicit  process 
of  the  major  or  minor  term,  not  of  the  major  or  minor 
'premiss. 

VII.  If  both  premisses  in  a  syllogism  be  particular  propo- 
sitions, we  can  draw  no  conclusion  ;  thus, 


94  LOGIC. 

1.  Some  men  are  wise, 

2.  Some  men  are  foolish, 

leads  us  to  do  conclusion.     Nor  are  we  benefited  if  we  make 
one  of  the  ipremisses  particular  negative;  thus, 

1.  Some  men  are  wise, 

2.  Some  men  are  not  brave, 

we  are  as  before  without  any  medium  of  comparison. 

The  fact  is  as  stated ;  the  causes  are  various,  and  will  be 
fully  explained  in  the  chapter  on  Figure. 

It  is  sufficient,  now,  for  the  student  to  know  that  the  cause 
is  in  every  case  either  an  undistributed  middle  or  an  illicit 
process  of  one  of  the  other  terms. 

By  the  foregoing  axioms  and  rules,  we  extend  the  range 
of  syllogistic  forms,  and  are  able  to  see  the  validity  or  inva- 
lidity of  an  argument  without  reducing  it  to  the  invariable 
formula  of  Aristotle's  dictum.  We  proceed  now  to  show  how 
many  of  these  forms  there  may  be,  and  the  relation  they  sus- 
tain to  the  dictum  itself;  and  this  brings  us  to  the  subject  of 
Figure  and  Moods. 


CHAPTER   VIII. 

OF  FIGURE  AND  MOODS. 

(38.)  Figure. 

Figure  is  the  technical  name  employed  to  designate  the 
classification  of  syllogisms  according  to  the  position  of  the 
middle  term  with  reference  to  the  two  extremes  in  the  premisses. 
Now,  it  is  evident  that  the  middle  term  can  have  only  four 
variations  of  position,  and  hence  we  say  there  are  four  figures. 

1st.  The  middle  term  may  be  the  subject  of  the  major 
premiss,  and  the  predicate  of  the  minor,  and  this  designates 
the  1st  figure. 

2d.  It  may  be  the  predicate  of  both  premisses,  and  thus  the 
2d  figure  is  designated. 

3d.  In  the  Sd  figure  it  is  the  subject  of  both  premisses ;  and 

4th.  In  the  -Uh  figure  (which  is  the  reverse  of  the  1st)  it  is 
the  predicate  of  the  viajor  premiss  and  the  subject  of  the  minor. 

If  we  designate  the  major  term  by  P  (as  it  is  always  the 
predicate  of  the  conclusion  »,  the  minor  term  by  S  (being  the 
subject  of  the  conclusion),  and  the  middle  term  by  M,  and 
merely  state  these  various  positions  of  the  middle  term,  with- 
out considering  or  denoting  the  quantity  or  quality  of  the 
propositions  in  the  syllogism,  we  shall  have  the  abstract  syl- 
logism. 


I. 

II. 

III. 

IV. 

M  is  P. 

P  is  M. 

Mis  P. 

P  isM. 

S   isM. 

S  is  M. 

M  is  S. 

M  is  S. 

S  isP 

Sis  P. 

S  is  P. 

S  is  P. 

These  are  called  the  four  figures;  and  to  the  syllogisms 
which  occur  in  them  the  axioms  and  rules  already  laid  down 
directly  apply. 

95 


i)S  LOGIC. 

If  now  we  proceed  to  exaniine  these  figures  in  order,  we 
shall  find  that  the  first  figure  is  but  the  symbolical  represen- 
tation of  Aristotle's  dictum,  the  simplest  form  of  the  syllogism. 
There  will  be  four  variations  of  it,  viz. : 

1.  2.  3.  4. 

All  M  is  P.  All  M  is  P.  No  M  is  P.  No  M  is  P. 

All  S  is  M.  Some  S  is  M.  All  S  is  M.  Some  S  is  M. 

All  S  is  P.  Some  S  is  P.  No  S  is  P.  Some  S  is  not  P. 

We  have  simply  supplied  the  quantity  and  quality  required. 

Since,  in  the  major  premiss,  then,  of  Aristotle's  dictum,  we 
assert  or  deny  the  predicate  of  the  whole  class  which  is  the  subject 
(All  M),  it  is  evident  that  in  the /rs^ /^i^re,  the  major  premiss 
is  always  universal.  If,  then,  with  this  relative  position  of  the 
middle  term,  i.  e.,  in  the  first  figure,  we  find  a  syllogism  the 
m,ajor  premiss  of  which  is  particular,  we  may  at  once  declare 
it  to  be  invalid. 

Again,  since  the  province  of  the  minor  premiss  in  the  dictum 
is  always  to  assert  that  certain  individuals  belong  to  the  given 
class  (and  in  no  case  to  deny  it),  it  appears  that  in  the  first 
figure  the  minor  premiss  must  always  be  affirmative^  so  that 
if  we  find  a  syllogism  in  this  figure  with  a  negative  minor 
premiss,  we  may  at  once  declare  it  invalid. 

Thus,  in  stating  the  four  forms  of  the  dictum,  we  have 
stated  the  only  four  forms  which  the  first  figure  can  cover. 

But  the  other  figures,  which  are  not  directly  in  the  form 
which  the  dictum  assumes,  instead  of  being  explained  by  it, 
are  to  be  considered  in  the  light  of  the  axioms  and  rules  for 
determining  the  validity  of  syllogisms  when  the  dictum  does 
not  directly  apply.     By  examining  the  second  figure, 

PisM, 

S  is  M, 
S  is  P, 

we  shall  find  that  there  are  several  forms  which  it  will  assume 
when  we  supply  the  quantity  and  quality  to  the  propositions 


FIGURE.  97 

We  observe  at  once  that  the  couclusion  must  iu  every  case  be 
negative,  because — 

1st.  The  middle  term  is  the  predicate  of  both  premisses. 

2d.  The  middle  term  must  he  distributed  at  least  once  in  the 
syllogism. 

3d.  In  order  that  the  predicate  of  a  proposition  shall  be 
distributed,  the  proposition  must  be  negative. 

4th.  This  will  give  us  one  negative  premiss,  and  by  the 
second  axiom,  if  we  have  a  negative  premiss,  the  conclimion 
must  be  negative  (^universal  or  particular). 

Third  Figure. 
M  is  P, 
MisS, 
S   is  P. 

By  the  supplying  of  quantity  and  quality,  this  figure  as- 
sumes a  greater  variety  of  forms  than  any  other. 

By  considering  the  position  of  the  terms  here,  it  will  appear 
that  we  can  only  draw  particular  conclusions.  For  if  both 
premisses  be  affirmative,  and  we  draw  a  universal  conclusion, 
or  All  S  is  P,  then  S  (the  minor  term),  which  was  undistrib- 
uted in  the  minor  premiss  (being  the  predicate  of  an  affirma- 
tive proposition),  will  be  distributed  in  the  conclusion,  as  the 
subject  of  a  universal ;  or  we  shall  have  an  illicit  process  of  the 
minor. 

If  the  major  premiss  be  negative,  and  we  draw  a  universal 
conclusion,  it  is  easily  shown  that  the  same  error — an  illicit 
process  of  the  minor — obtains ;  and  if  the  minor  premiss  be 
negative,  we  shall  have  an  illicit  process  of  the  major. 

Fourth  Figure. 
P  is  M, 
MisS, 
S   is  P. 

The  fourth  figure,  which  was  not  proposed  by  Aristotle  with 
Che  other  three,  and  only  recently  adopted  by  logicians,  is  an 
«  G 


98  LOGIC. 

inversion  of  the  first,  and  an  unnatural  and  unnecessary  tbrui 
of  the  syllogism.  By  a  similar  examination  of  all  the  terms, 
we  shall  find  that  we  may  draw,  as  conclusions,  in  this  figure 
all  the  categorical  propositions  except  A,  which,  as  has  been 
shown,  can  only  be  drawn  in  the  first  figure.  It  is  the  pre- 
rogative of  Aristotle's  dictum  alone,  to  draw  from  certain 
premisses  a  universal  affirmative  conclusion. 

The  various  forms  of  the  syllogism  due  to  the  diflferent 
quantity  and  quality  of  the  propositions  composing  them  are 
arranged,  in  the  different  figures,  in  what  are  called  moods,  or 
a  concise  manner  of  expressing  a  syllogism  by  symbols. 

(39.)  Of  Mood. 
If,  having  any  syllogisms,  as  the  following — 

r  All  A  is  B,     (A)  rNoAisB,  (E) 

1.  ■]  All  C  is  A,     (A)  2.  }  Some  C  is  A,  (I) 

(  All  C  is  B,     (A)  (  Some  C  is  not  B,     (O) 

we  write  together  the  symbols  characterizing  each  proposition 
which  composes  them,  we  are  said  to  determine  the  mood  of 
the  syllogism ;  thus,  the  symbol  of  the  major  premiss  in  the 
first  syllogism  is 

A,  or  universal  affirmative ; 
that  of  the  minor, 

A,  or  universal  affirmative ; 

and  that  of  the  conclusion  likewise 

A,  or  universal  affirmative. 

Hence  we  say  that  A  A  A  is  the  mood  of  the  syllogism. 

In  the  second  syllogism,  we  shall  find  by  a  similar  process 
that  the  mood  is  E I  0. 

Now  it  is  evident  that  the  number  of  moods  we  can  have 
will  depend  upon,  1st,  the  number  of  propositions  in  the  syl- 
logism, viz.,  three;  and  2d,  upon  the  number  of  categorical 
propositions  which  we  can  enumerate,  viz. ,  four.  A,  E,  I,  O ; 


FIGURK.  99 

it  becomes  then  a  simple  algebraic  arrangement  of  four  letters, 
A,  E,  J,  O,  in  three  columns  in  every  possible  combination. 
The  number  of  these  possible  combinations  will  be  sixty-four 
For  each  of  the  propositions  A,  E,  I  and  O  may  have  a  major 
premiss;  and  each  of  these  may  have  each  in  turn  as  a  miner 
premiss ;  thus, 

Mqj.  prem.    Maj.  prem.    Maj.  pi-em.    Maj.  prenu 
A  E  I  O 


I    I    I    I       I    I    I    I       I    I    I     I       I    I    I    I 

may  have  as  miuor  premisses,      AEIO       AEIO      AEIO      AEIO 

Again,  each  of  these  sets  (sixteen  in  all)  may  have  four 
different  conclusions,  i.  e.,  each  of  the  categoricals  as  a  con- 
clusion. Taking  the  first  set,  for  example,  and  supposing  the 
operation  performed  for  the  rest: 

FIRST   SET. 

Maj.  prem.  A. 


Min.  prem.      AEIO 


I       I      I       I         I       I       I      1         I       I       I      I         I       I      I      I 
Cond.     AEIO       AEIO       AEIO      AEIO 

This  same  process  may  be  performed  for  E,  I  and  O. 
There  will  evidently  be  sixty-four  moods,  of  which,  however,  it 
is  at  once  evident  that  very  many  will  violate  the  axioms  and 
rules  already  laid  down,  and  must  be  for  this  reason  discarded. 

Thus,  all  the  combinations  of  affirmative  premisses  having 
negative  conclusions,  as  A  A  E,  A  I  O,  etc.,  etc.,  must  be 
thrown  aside,  because  they  violate  the  first  axiom. 

Ail  the  sets  of  negative  premisses,  with  whatever  conclu- 
sions, are  useless,  as  E  E,  O  O,  E  O,  O  E,  etc. 

All  the  sets  of  particular  premisses,  with  whatever  conclu- 
sions, must  be  neglected,  such  as  I  I,  O  O,  O  I,  I  O,  etc. 

If  all  these  eliminations  be  performed — and,  simple  as  they 
are,  the  student  is  advised  to  go  carefully  through  them  once 
for  himself — we  .-hall  find  twenty-eight  moods  excluded  on  ac 


lOU  LOGIC. 

count  of  negative  and  particular  premisses :  eighteen  by  the 
condition  that  the  conclusion  follows  the  inferior  part,  and  we 
shall  see  that  one— I  E  O — is  rejected  for  an  illicit  process  of 
the  major  term,  in  every  figure,  and  finally  that  of  the  sixty- 
four  arrangements  which  we  call  moods,  only  eleven  represent 
valid  arguments,  or 


FOUR   AFFIRMATIVES 

AND   SEVEN  NEGATIVES. 

AAA 

E 

A 

E 

All 

A 

E 

E 

A    A     I 

E 

A 

0 

I     A     I 

A 

0 

0 

0 

A 

0 

E 

I 

0 

A 

E 

0 

If  now  we  apply  these  moods  to  each  figure,  in  detail,  it 
would  seem,  since  there  are  four  figures,  that  we  should  have 
4  X  11  =  44  moods  in  all  the  figures  ;  but  in  this  application 
we  find  that  many  moods  which  are  valid  in  one  figure  are 
not  in  others ;  as,  for  example,  the  mood  I  A  I,  which  is 
allowable  in  the  third  figure,  would  be  in  the  first  figure  a 
case  of  undistributed  middle,  and  would  further  violate  the 
principle  of  Aristotle's  dictum,  which  requires  that  the  majoi 
premiss  should  be  a  universal  proposition.  A  E  E  is  a  valid 
mood  in  the  second  figure,  while,  in  i\ie,  first,  it  would  have  an 
illicit  process  of  the  major  term,  and  would  further  violate 
that  principle  of  the  dictum  which  requires  the  minor  premiss 
to  be  always  affirmative. 

By  applying  these  eleven  moods  to  the  four  figures,  we  find 
that  there  would  be  six  in  each  figure,  or  twenty-four  in  all; 
but  even  of  these,  five  are  omitted  as  useless ;  for  example, 
the  mood  A  A  I,  in  the  first  figure,  because  it  is  implied  and 
contained  in  the  mood  AAA.  Since,  if  the  universal  con- 
clusion A  be  true,  the  particular  I  is  necessarily  true.  By 
an  application  of  each  of  these  moods  to  every  figure,  we 
shall  have  left,  filially,  nineteen  moods  in  all ;  or,  lOUR  in  the, 


FIGURE.  101 

first  figure,  four  in  the  second,  six  ui  t/ie  third,  and  five  in 
the  fourth. 

The  moods  of  the  first  figure  are  called  perfect  moods  -,  thost 
in  the  other  figures,  imperfect  moods. 

As  it  has  been  asserted  that  all  arguments  may  be  put  iu 
the  form  of  Aristotle's  dictum,  that  is,  that  all  the  imperfect 
moods  may  be  made  perfect,  we  proceed  to  fulfill  this  asser- 
tion, by  the  process  of  reduction,  i.  e.,  the  reducing  of  moods 
in  the  2d,  3d,  and  4th  figures  to  the  1st  figure,  which  is  the 
form  of  the  dictum. 

In  order  to  facilitate  this  process,  as  well  as  to  retain  easily 
in  the  memory  the  different  moods  and  their  value,  the  fol- 
lowing verses,  Latin  in  sound  and  scansion,  but  without  in- 
trinsic meaning  in  the  words,  have  been  formed : 

Fig.  I.— BArbArA,  CElArEnt,  DArll,  FErlO,  dato  primce. 
Fig.  II.— CEsAKE,  CAmEstrEs,  FEstInO,  FAkOrO,  secundcs. 
„       TfT  _  I  "Tertia  DArAptl,  DIsAmIs,  DAtlsI,  FElAptOn, 
1  DOk AmO,  FErlsO,  habet ;  quarta  insuper  addit. 
Fig.  IV.— BrAmAntIP,  CAmEnEs,  DImArls,  FEsApO,  FrEsIsOn. 

There  are  variations  in  these  lines,  made  by  various  writers  ; 
we  have  adopted  the  above  as  the  form  which  will  indicate  to 
us  in  the  simplest  manner  the  processes  of  Reduction. 

Before  explaining  these  lines,  which  the  student  must  mem- 
orize in  order  to  make  them  useful,  that  he  may  have  the 
moods,  and  their  places  in  the  figures,  at  his  tongue's  end,  it 
will  be  observed  that  there  are  a  few  words  used  in  these 
verses  which  are  of  no  use  except  to  make  out  the  hexameter 
lines;  of  these  are  dato  primce  in  the  first,  secundce  in  the 
gocond,  tertia  habet  in  the  third,  and  quarta  in.mper  addit, 
which  states — moreover  the  fourth  adds,  etc.  Leaving  tliese 
out  of  the  consideration,  in  the  lines  themselves  the  vowels  in 
each  word  represent  the  moods;  thus,  Barbara  is  the  mood 
AAA;   Cesare,  the  mood  E  A  E,  etc.,  etc. 

The  following  consonants  indicate  what  chancres  are  to  be 


102  LOGIC. 

made  in  the  given  •imperfect  mood  to  reduce  it  to  a  perfea 
mood  of  the  first  figure: — s,  that  the  proposition  indicated  by 
the  vowel  immediately  preceding  it  is  to  be  converted  simply : 
thus  in  Camestres,  the  first  s  indicates  the  simple  conversion 
of  the  first  E,  or  the  minor  premiss,  and  the  last  s  the  simple 
conversion  of  the  second  E,  or  the  conclusion.  In  similar 
relations  p  and  k  stand  respectively  for  conversion  by  limitation 
and  conversion  by  negation ;  m,  wherever  it  occurs,  expresses 
that  the  premisses  must  be  transposed  ;  the  other  consonants 
have  no  meaning,  and  are  only  employed  to  frame  the  words. 
P,  in  the  mood  Bramantip  of  the  fourth  figure,  denotes  that 
the  transposed  premisses,  indicated  by  m,  will  warrant  a  uni- 
versal conclusion  instead  of  a  particular.  The  initial  letters, 
B,  C,  D,  F,  of  the  words  which  contain  the  moods,  are  so 
arranged  throughout  the  figures  as  to  indicate  the  mood  in 
the  first  figure  to  which  any  imperfect  mood  will  be  reduced; 
thus  Darapti  of  the  third  figure  will,  when  reduced,  become 
Darii  of  the  first,  Camestres  will  become  Celarent,  etc. 

It  must  be  observed  that  this  arrangement  is  only  for  the 
sake  of  convenience,  as  the  process  of  reduction  is  invariable, 
and  the  mood  Darapti  would  become,  when  reduced,  the  mood 
A  I  I  of  the  first  figure,  whether  it  were  called  Darii  or  by 
some  other  name.  Students  are  apt  to  be  misled  with  refer- 
ence to  these  initial  letters,  and  to  suppose  that  they  will  aid 
them  in  the  process  of  reduction.  It  is  on  this  account  that 
they  are  cautioned  that  this  is  only  a  convenient  and  not  an 
auxiliary  arrangement.  Before  proceeding  to  explain  the 
system  of  reduction,  let  us  give  an  example  of  each  mood,  in 
all  the  figures,  putting  the  logical  frame-work  to  its  legitimate 
use,  and  showing  every  form  which  the  syllbgism  can  assume. 
We  shall  make  the  examples  very  simple,  leaving  it  to  the 
student,  with  these  before  him,  to  frame  longer  and  more 
complex  ones  for  himself — a  practical  exercise  which  will  be 
found  very  useful.  The  middle  term  is  placed  in  italics  in 
each  example. 


FIGURE.  103 

Examples. 

FIGURE   I. 

Barbara. 

A.  Every  desire  to  gain  by  another's  loss  is  covetousnesa 
A.  All  gaming  is  a  desire  to  gain  by  another's  loss. 
A.  All  gaming  is  covetousness. 

Celarent. 

E.  No  one  who  is  enslaved  by  his  appetites  is  free. 

A.  Every  sensualist  is  one  who  is  enslaved  by  his  appetites. 

E.  No  sensualist  is  free. 

Darii. 

A.  All  pure  patriots  deserve  the  rewards  of  their  country. 

I.    Some  warriors  are  pure  patriots. 

I.    Some  warriors  deserve  the  rewards  of  their  country. 

Ferio. 

E.  Nothing  which  impedes  commerce  is  beneficial  to  the 
revenue. 

I.  Some  taxes  impede  commerce  (or  are  things  which  impede 
commerce). 

O.  Some  taxes  are  not  beneficial  to  the  revenue. 

FIGURE   II. 

Cesare. 
E.  No  vicious  conduct  is  praiseworthy. 
A.  All  truly  heroic  conduct  is  praiseworthy. 
E.  No  truly  heroic  conduct  is  (or  can  be)  vicious. 

Camestres. 
A.  Every  true  philosopher  accounts  virtue  a  good  in  itself. 
E.  No  advocate  of  pleasure  accounts  virtue  a  good  in  itself. 
E.  No  advocate  of  pleasure  is  a  true  philosopher. 


104  LOGIC. 

The  true  middle  term  here  would  be  {one  who)  accounU 
virtue  a  good  in  itself. 

Festino. 
E.  No  righteous  acts  will  produce  ultimate  evil  to  the  actor, 
I.    Some  kinds  of  association  will  produce  ultimate  evil  tc 
the  actor. 

O.  Some  kinds  of  association  are  not  righteous  acts. 

Fakoro. 
A.  All  true  patriots  slyq  friends  to  religion. 
O.  Some  great  statesmen  are  not  fnends  to  religion. 

0.  Some  great  statesmen  are  not  true  patriots. 

FIGUKE   III. 

Darapti. 

A.  All  wits  are  dreaded. 
A.  All  wits  are  admired. 

1.  Some  admired  (persons)  are  dreaded. 

Disamis. 
I.    Some  lawful  things  are  inexpedient. 
A.  All  lawful  things  are  what  we  have  a  right  to  do. 
I.    Some  things  which  we  have  a  right  to  do  are  inexpe- 
dient. 

Datisi. 

A.  All  that  wisdom  dictates  is  right. 

I.    Something  that  urisdom  dictates  is  amusement. 

I.    Some  amusement  is  right. 

Felapton. 
E.  No  sde7ice  is  capable  of  perfection. 
A.  All  science  is  worthy  of  culture, 

O.  Something  worthy  of  culturf  is  not   capable  of  pei 
fection. 


FIGURE.  lOo 

Dokamo. 
O.  Some  nohle  characters  are  not  philosophers. 
A.  All  noble  characters  are  worthy  of  admiration. 

0.  Some  (who  are)  worthy  of  admiration  are  not  philoso 
phers. 

Feriso. 

E.  No  false  theories  exist  in  a  perfect  state  of  being. 

1.  Some  false  theories  are  harmless  things. 

0.  Some  harmless  things  do  not  exist  in  a  perfect  state  of 
being. 

FIGURE   IV. 

Bramantip. 

A.  All  oaks  are  trees. 

A.  All  trees  are  vegetables. 

1.  Some  vegetables  are  oaks.  | 

Camenes. 

A.  All  men  are  mortal. 
E.  No  mortal  is  a  stone. 
E.  No  stone  is  a  man. 

Dimaris, 

I.    Some  taxes  are  oppressive. 

A.  All  {that  is)  oppressive  should  be  repealed. 

I.    Some  things  which  should  be  repealed  are  taxes. 

Fesapo. 
E.  No  immoral  acts  are  proper  amusements. 
A.  All  proper  amusements  are  designed  to  give  pleasure. 
O.  Some  (things)  designed  to  give  pleasure  are  not  im- 
moral acts. 

Fresison. 

E.  No  acts  of  injustice  are  proper  means  of  self-advance- 
ment. 


106  LOGIC. 

I.  Some  proper  means  of  self-advancement  are  unsuccessful 

O.  Some  unsuccessful  (eflbrts)  are  not  acts  of  injustice. 

It  will  be  observed  that  the  conclusions  in  the  fourth  figure 
are  indirectly  stated,  and  that  it  would  seem  as  if  in  tracing 
the  major  term  back  from  its  place  as  predicate  of  the  con- 
clusion, it  is  in  reality  predicated  by  means  of  the  other 
terms  of  itself;  thus,  in  the  conclusion  it  is  predicated  of  the 
minor,  which  in  the  minor  premiss  is  predicated  of  the  mid- 
dle, which  in  the  major  premiss  is  predicated  of  the  major. 
The  fourth  figure,  therefore,  is  not  often  used,  and  is  rather 
accidentally  stumbled  into  than  employed  intentionally. 

The  exact  accordancy  of  the  first  figure  with  the  dictum 
of  Aristotle  has  been  already  stated.  Of  the  second  figure, 
it  may  be  remarked  that  it  is  commonly  used  to  disprove 
something  that  has  been  maintained,  or  is  likely  to  be  be- 
lieved, although  not  true.  As  an  illustration,  suppose  it  had 
been  asserted  that 

All  great  statesmen  are  true  patriots. 

Then  our  example  just  given  of  Fakoro  would  be  a  refuta- 
tion of  this,  and  the  argument  would  naturally  take  that 
form. 

Of  the  third  figure,  it  will  appear  that  it  will  be  useful 
where  we  have  singular  terms,  which  can  only  be  subjects  of 
propositions — i.  e.,  never  predicates — and  also  where  our  pur- 
pose is  to  offer  and  sustain  an  objection  to  our  opponent's 
premiss,  which  is  particular  when  the  argument  requires  it  to 
be  universal. 

There  are  very  many  inverted  and  curious  forms  of  argur 
ments  growing  out  of  the  elliptical  and  inverted  forms  of 
propositions,  which  we  have  already  considered.  Two  com- 
mon examples  of  these  are  added  by  way  of  illustration. 

1. 
None  but  whites  are  civilized. 
The  Hindoos  are  not  whites. 
The  Hindoos  are  not  civilized. 


OF    REDUCTION.  107 

The  phrapie  none  hut   whiles  may  be  rendered,  oiher  iluin 
whiles;  and  this  being  the  true  middle  term,  we  shall  have — 

No  ofW  than  whitets  are  civiliz€*L 
All  Hindoos  are  otfi£r  iluin  vikiUn. 
No  Hindoos  are  civilized. 

Which  is  evidently  a  syUogism  in  Celarent  of  the  fird  figure. 

2. 
No  one  is  rich  who  has  not  enough. 
No  miser  has  enough. 
•  No  miser  is  rich. 

The  major  and  minor  premisses  must  be  put  in  the  form 
of  categorical  propositions,  and  we  shall  have — 

No  one  who  has  not  enoiigh  is  rich. 
Ever}'  miser  is  one  who  has  not  enough. 
No  miser  is  rich. 

Which  is  likewise  in  the  mood  Celarent.  In  both  these  ex- 
amples the  minor  premiss,  which,  appears  to  be  a  negative 
proposition,  is  in  reality  affirmative. 

(40.    Of  Reduction. 

If  we  have  any  imperfect  mood — i.  e.,  a  mood  in  the  sec- 
ond, third,  or  fourth  figure — and  we  desire  to  prove  the  same 
conclusion  in  the  first  figure,  so  that  the  dictum  of  Aristotle 
may  immediately  be  applied  to  it,  the  process  by  which  this 
is  done  is  called  Reduction. 

Beduction  is  of  two  kinds,  direct  and  indirect.  Direct 
reduction  consists  in  proving  in  a  perfect  mood  either  the 
same  conclusion,  or  one  which,  being  illatively  converted, 
will  give  us  the  same  conclusion  which  we  had  in  the  imper- 
fect mood.  Indirect  reduction  consists  in  proving,  not  that 
the  original  conclusion  />  true,  but  that  its  cordradidxjry  it 
false,  from  which — by  the  scheme  of  opposition — we  kno^ 
that  the  original  conclusion  must  be  true. 

Of  direct  reduction. 

It  has  been  shown  that  we  have  a  right  to  convert  any  of 


l')8  LOGIC. 

the  propositions  of  the  syllogisni  illatively ;  and  it  is  also 
evident  that  we  may  transpose  the  premisses  without  affecting 
the  truth  of  the  propositions  or  the  validity  of  the  argument. 
If,  then,  we  apply  the  processes  indicated  by  the  letters  in 
the  mnemonic  lines,  we  shall  see  that  they  will  give  us  the 
forms  of  direct  reduction. 

Taking  for  example  Cesare,  the  mood  E  A  E  in  the  sec- 
Dud  figure ;  to  write  it  out  we  remember  in  the  first  place  that 
the  position  of  the  middle  term  in  the  second  figure  is  predi- 
cate of  both  premisses,  and  we  observe  that  the  major  premiss 
is  E,  universal  negative,  the  minor  premiss  A,  universal 
afiirmative,  and  the  conclusion  E,  universal  negative;  we 
have  then  X,  being  the  major,  Z  the  minor  and  Y  the  mid- 
dle term — 

Cesare.    Fig.  II. 

E.  No  X  is  Y  =  No  men  are  trees. 
A.  All  Z  is  Y  =  All  oaks  are  trees. 
E.     No  Z  is  X  =  No  oaks  are  men. 

The  only  consonant  in  the  word  CEsArE  which  indicates 
a  process  of  reduction  is  s,  which  tells  us  that  the  major 
premiss,  expressed  by  the  first  E,  is  to  be  simply  converted  ; 
performing  this  operation  we  shall  have — 

Celarent.    Fig.  I. 

E.  No  Y  is  X  =  No  trees  are  men. 
A.  All  Z  is  Y  =  All  oaks  are  trees. 
E.     No  Z  is  X  =  No  oaks  are  men. 

This  syllogism  is  in  the  first  figure,  since  the  middle  term 
V  or  trees  has  become  the  subject  of  the  major  and  the  pred- 
icate of  the  minor  premiss ;  again, 

Fakoro.     FiG.  II. 
A.     All  X  is  Y  =  All  good  men  are  virtuous. 

O.     Some  Z  is  not  Y  =  Some  warriors  are  not  virtuous. 
O.     Some  Z  is  not  X  =  Some  warriors  are  not  good  men. 

The  k  expresses  that  the  major  premiss  (A)  is  to  be  converted 
by  negation;  performing  this  operation  (there  is  no  othei 
indicated),  we  shall  have — 


OF    REDUCTION.  109 

Ferio.     Fig.  I. 
E.     All  (not  Y)  is  not  X  =  All  (not  virtuous)  are  not  goo<i  men. 
I.      Some  Z  is  (not  Y)      =  Some  warriors  are  (not  virtuous). 
O.     Some  Z  is  not  X         =  Some  warriors  are  not  good  men. 

This  process,  in  effect,  changes  our  middle  terra  from  Y  oi 
virtuous  to  Knot  Y)  or  {jiot  virtuous),  while  \Ye  have  the  same 
conclusion  as  before  in  the  mood  Ferio  of  the  first  figure. 

The  reduction  of  the  other  moods  of  the  second  figure  will 

be  analogous  to  those  already  performed,  and  the  student 

will  find  no  difficulty  in  reducing  them  for  himself.     Passing, 

then,  to  the  third  figure,  and  remembering  that  in  this  figure 

the  middle  term  is  the  subject  of  both  premisses,  let  us  reduce 

the  mood 

Disamis.     Fig.  III. 

I.      Some  Y  is  X  :=  Some  men  are  heroes. 

A.     All  Y  is  Z       =  All  men  are  mortal. 

I.      Some  Z  is  X  =  Some  mortals  are  heroes. 

The  two  letters  which  indicate  changes  in  the  process  of 
reducing  this  mood  are  s  (twice  employed)  and  m:  s  indicates 
the  simple  conversion  of  the  major  premiss  and  the  conclu- 
sion, and  m  the  transposition  of  the  premisses ;  performing 
these  operations,  we  have 

Darii.     FiG.  I. 
A.   All  Y  is  Z       =^  All  men  are  mortal. 
I.     Some  X  is  Y  =  Some  heroes  are  men. 
I.    Some  X  is  Z  ^  Some  heroes  are  mortal. 

Which  conclusion  is  the  simple  converse  of  the  original  con- 
clusion, as  was  indicated  by  the  final  s. 

Fesapo.     FiG.  IV. 
A.     No  X  is  Y  =  No  quadrupeds  are  men 

E.     All  Y  is  Z  =  All  men  are  animals. 

O.     Some  Z  is  not  X  =  Some  animals  are  not  quadrupeds. 

Converting  the  major  preraiss  simply,  and  the  minor  premiss 
by  limitation,  as  indicated  by  the  s  and  p,  we  shall  have 

10 


no 


LOGIC. 


Ferix).     Fig.  I. 
E.     No  X  is  Y  =  No  men  are  quadrupeds. 

I.      Some  Z  is  Y         =  Some  animals  are  men. 
O.     Some  Z  is  not  X  =  Some  animals  are  not  quadrui<eds. 

It  will  be  well  for  the  student  to  reduce  every  imperfecl 
mood,  forming  for  himself  particular  examples  under  each. 

Although  we  have  made  the  subject  of  Reduction  plain  by 
the  examples  already  given,  we  append  a  table  of  the  man- 
ner  of  reducing  each  mood  for  reference,  until  the  student  is 
familiar  with  them.  It  is  but  a  recapitulation  in  tabular  form 
of  what  has  been  already  explained. 


Mood  to  be  reduced. 


Fig.  II.    \ 


Cesare. 

Camestres. 

Festino. 
Fakoro. 

Darapti. 

Disamis. 

Fig.  III.  -!  Datisi. 

Felapton. 

Dokamo. 
^  Feriso. 


Bramantip. 


Will 
reduce. 


Process  of  Reduction. 


Celarent.  (s)  Convert  major  premiss  simply. 

(m)  Transpose  the  premisses,  (s&s) 
Convert  the  minor  premiss  and 
conclusion  simply. 

(s)  Convert  the  major  premiss  simply. 

(k)  Convert  the  major  premiss  by  ne- 
gation. 


Celarent. 

Ferio. 

Ferio. 


Fig.  IV.  -j 


Camenes. 

Celarent. 

Dimaris. 

Darii. 

Fesapo. 

Ferio. 

Fresison. 

Ferio. 

Darii. 

Darii. 

Darii. 
Ferio. 

Darii. 

Ferio. 

Barbara. 


(p)  Convert  the  minor  premiss  by 
limitation. 

(m)  Transpose  the  premisses,    (s&s) 

Convert  the  major  premiss  and 

conclusion  simply. 

s)  Convert  the  minor  premiss  simply. 

p)  Convert  the   minor   premiss   by 

limitation. 

(k)  Convert  the  major  premis  by  ne- 
gation, (m)  Transpose  the  pre- 
misses. 

(s)  Convertthe  minor  premiss  simply. 

(m)  Transpose  the  premisses,  (p) 
Convert  the  conclusion  by  lim- 
itation. 

(ml  Transpose  the  premisses.  (s) 
Convert  the  conclusion  simply. 

(m)  Transpose  the  premisses.  ,^s) 
Convert  the  conclusion  simply. 

(s)  Convert  the  major  premiss  simply. 
(p)  Convert  the  minor  premiss 
by  limitation. 

(s  &  s)  Convertthe  major  and  minoi 
premisses  simply. 


INDIRECT    REDUCTION.  Hi 

(41.)  Indirect  Reduction. 

This  process,  called  by  the  old  logicians  Redadio  ad  impos- 
iible,  is  analogous  to  the  reductio  ad  absurdum  of  geometry. 
It  consists  in  proving  that  the  given  conclusion  cannot  be 
false  by  proving,  in  the  first  figure,  that  its  contradictory  is 
false. 

The  symbols  used  to  indicate  the  processes  of  direct  reduc- 
tion do  not  guide  us  in  the  indirect  reduction,  but  we  must 
deduce  rules  for  this  apart  from  the  other. 

To  illustrate,  let  us  take  the  mood 

Fakoro.     FiQ.  II. 

A.    All  X  is  Y  =  All  good  men  are  virtuous. 

O.     Some  Z  is  not  Y  =  Some  warriors  are  not  virtuous. 

O.     Some  Z  is  not  X  =  Some  warriors  are  not  good. 

If  this  conclusion  be  not  true,  its  contradictory  All  Z  is  X  = 
All  warriors  are  good,  must  be  true.  Assuming  this  as  true, 
and  taking  it  in  the  place  of  the  minor  premiss  in  the  syllo- 
gism, we  shall  have  a  new  syllogism,  as  follows : 

A.     All  X  is  Y  =  All  good  men  are  virtuous. 
A.     All  Z  is  X   =  All  warriors  are  good  men. 

from  which  premisses  by  our  rules  we  draw  the  conclusion 

A.     All  Z  is  Y  =  All  warriors  are  virtuous. 

But  this  conclusion  must  be  false,  because  it  is  the  contradic- 
tory of  the  original  minor  premiss,,  and  the  premisses  were 
assumed  to  be  true ;  hence  one  of  these  last  premisses  from 
which  this  conclusion  is  derived  must  be  false ;  but  it  is  not 
the  major,  for  that  was  one  of  the  originally  assumed  premis- 
ses; it  must,  therefore,  be  the  minor,  which  we  know  to  be 
the  contradictory  of  our  original  conclusion  ;  and  the  original 
conclusion  must  therefore  be  true:  this,  it  will  be  observed,  is 
proven  in  the  first  figure,  in  the  mood  Barbara.  To  take 
another  example,  let  us  reduce  the  mood 


112  LOGIC. 

Darapti.    Fig.  III. 
A.    All  Y  is  X     =  All  gold  is  precious. 
A.     All  Y  is  Z      =  All  gold  is  a  mineral. 
I.      Some  Z  is  X  =  Some  mineral  is  precious. 

If  this  conclusion  be  not  true,  then  must  its  contradictory, 

No  Z  is  X  =  No  mineral  is  precious, 
be  so.     Suostituting  this  as  the  major  premiss  in  the  syllo- 
gism, we  have 

No  Z  is  X  =  No  mineral  is  precious. 
All  Y  is  Z  =  All  gold  is  a  mineral. 

From  which  we  draw  the  new  conclusion 

No  Y  is  X  =  No  gold  is  precious. 

But  this  conclusion  is  false,  because  it  is  the  contrary  of  the 
original  major  premiss,  which  we  assume  to  be  true ;  one  of 
the  premisses  from  which  it  was  derived  must  be  therefore 
false :  it  cannot  be  the  minor,  which  was  also  assumed  to  le 
true ;  it  must,  therefore,  be  the  major,  which  is  the  contradit 
tory  of  the  original  conclusion ;  hence,  the  original  conclu- 
sion must  be  true. 

It  will  occur,  in  reducing  many  of  the  moods  by  this  pro- 
cess, as  in  the  last  example,  that  we  shall  find  the  conclusion 
fake,  because  it  is  the  contrary  and  not  the  eontradictory  of 
one  of  the  original  premisses.  By  referring  to  the  subject  of 
Opposition  (30),  we  see  that  if  one  contrary  is  true  the  other 
must  be  fake. 

Without  presenting  a  greater  number  of  examples  of  this 
kind  of  reduction,  which  the  student  may  multiply  for  him- 
self, we  lay  down  the  following  rules  for  reducing  the  varicjus 
imperfect  moods. 

Rules  for  Indirect  Reduction. 
Ist.  In  the  second  figure,  substitute  the  contradictory  of  the 
conclusion  for  the  minor  premiss,  and  proceed  as  above  in  the 
mood  Fakoro. 


INDIRECT    REDUCTION. 


113 


2d.  In  the  third  figure,  substitute  the  contradictory  of  the 
conclusion  for  the  major  premiss,  and  proceed  as  with  the 
mood  Darapti. 

3d  In  the  fourth  figure,  substitute  the  contradictory  of  the 
conclusion  for  the  minor  premiss,  and  proceed  as  before.* 

As  reference  is  always  easier  to  a  tabular  form,  we  annex 
one  showing  in  what  perfect  mood  the  indirect  reduction  of 
each  imperfect  mood  will  take  place : 


Fig.  II. 

Fig.  III. 

Fig.  IV. 

Cesare  to  Ferio. 

Darapti  to  Celarent. 

Bramantip  to  Celarent 

Camestres  to  Darii. 

Disamis  to  Celarent. 

Camenes  to  Darii. 

Festino  to  Barbara. 

Felapton  to  Barbara. 

Dimaris  to  Celarent. 

Fakoro  to  Barbara. 

Datisi  to  Ferio. 

Fesapo  to  Celarent. 

Dokamo  to  Barbara. 

Fresison  to  Celarent. 

Feriso  to  Darii. 

Before  proceeding  to  consider  the  irregular,  informal  and 
compound  syllogisms,  we  pause  to  show  the  method  of  geo- 
metrical notation,  already  referred  to,  by  which  the  pure 
syllogism  may  be  expressed. 

(42.)  Notation  of  the  Syllogism, 
As  there  subsists  in  the  mathematics  such  a  relation  of 
analysis  to  geometry,  as  that  most  analysis  is  capable  of  geo- 
metrical construction,  and  every  form  of  geometry  may  be 
stated  analytically  in  terms  of  its  equation,  so  mathematical 
logicians  have  attempted  to  make  for  the  analysis  or  symbolic 
form  of  the  syllogism  such  a  geometrical  notation  as  shall  at 
a  glance  represent  to  the  eye,  in  areas  of  limited  space,  what 
the  symbols  do  to  the  mind.  Indeed,  the  idea  is  so  simple 
that  we  have  already  illustrated  the  dictum  of  Aristotle 
through  its  agency.  Many  writers,  however,  have  been  in- 
clined to  go  too  far  in  its  use. 

*  Except  in  cases  of  Bramantip  and  Dimaris,  in  which  the  contradie- 
lory  Lb  substituted  for  the  major  premiss,  and  the  conclusion  simply  con- 
verted. 

10  *  H 


114  LOGIC. 

The  schemes  of  notation  best  known  are  those  of  Euler 
Ploucquet  and  Lambert,  and  the  more  complete  one  of  Sii 
William  Hamilton.  This  latter,  however,  passing  beyond 
our  needs,  is  suited  to  such  changes  as  would  result  from  the 
introduction  of  the  new  analytie;  and,  as  we  have  advisedly 
declined  to  place  that  system  in  our  text-book,  it  is  sufficient 
to  mention  Sir  W.  Hamilton's  scheme  without  explaining  it. 
In  a  more  extended  historical  treatise  it  would  demand  a 
special  consideration.  We  can  here  only  explain  what  we 
mean  to  use. 

Euler's  scheme  of  notation  is  altogether  the  one  best  suited 
to  our  purpose,  and  we  shall  limit  ourselves  to  the  explanation 
of  that.  It  is  essentially  an  arrangement  of  three  drdes,  to 
represent  the  three  terms  of  a  syllogism,  and,  by  their  com- 
bination, the  three  propositions.  Thus,  if  we  have  the  judg- 
ment 

All  men  are  mortal, 

we  know  that  under  this  class — all  men — are  included  many 
species  and  individuals  ;  as,  for  example,  all  Americans.  Kep- 
resenting,  then,  the  sphere  of  the  conception  mortal  by  a  circle, 
placing  within  this  circle  a  smaller  one,  wholly  contained  in 
it,  as  the  sphere  of  all  men,  and  yet  a  smaller  one,  wholly 
contained  in  this  latter,  as  the  sphere  of  all  Americans^  we 
shall  have — 


which  is  the  notation  of  a  syllogism  in  BArbA.rA.  By 
similarity  of  process,  we  shall  represent  the  syllogism  in 
CElA^rEnt: 


INDIRECT    REDUCTION. 


116 


No  A  is  B, 
All  C  is  A, 
No  C  is  B. 


DArll  will  be  thus  expressed: 


All  A  is  B, 
Some  C  is  A, 
Some  C  is  B. 


Here  it  is  evident  that  it  is  only  that  some  C  ivhich  is  contained 
in  A  that  we  have  a  right  to  assert  is  also  contained  in  B, 
although  other  portions  of  C  may  by  chance  be  also  contained 

in  B.     FErlO : 

No  A  is  B, 

Some  C  is  A, 
(1)  Some  C  is  not  B. 


Here  two  cases  are  presented — where  no  C  is  B  and  where 
some  C  is  B — neither  of  which  affects  the  truth  of  the  conclu- 
sion that  some  C  is  not  B.  We  have  only  applied  this  scheme 
to  the  first  figure,  but  by  this  simple  notation  of  Euler  every 
syllogism  in  the  other  figures  may  be  represented  to  the  eye, 
and  made  clear  to  those  who  are  much  f^uicker  at  geometry 


116 


LOGIC. 


than  at  analytical  work.     Take  for  example  Darapti  of  the 
third  figure : 


All  A  is  B, 
All  A  is  C, 
Some  C  is  B 


But  besides  this  representation  of  valid  syllogisms,  this 
system  exposes  at  once  fallacious  arguments  and  acts  as  a 
test  upon  a  test  of  their  unsoundness.  Take  for  example  the 
case  of  illicit  process  of  the  major  term : 


All  quadrupeds  are  animals, 
A  bird  is  not  a  quadruped, 
A  bird  is  not  an  animal. 


In  which  the  figure  denies  the  conclusion  by  allowing  the 
premisses,  and  yet  showing  that  birds  are  contained  under 
the  genus  animal.  Or  if  we  take  the  case  of  the  negative 
premisses : 

No  A  is  B, 
No  C  is  A, 


the  figure  shows  us  that  there  is  no  relation  whatever  estab- 
lished between  or  among  the  terms  which  would  entitle  us  to 
a  conclusion. 

The  student  will  find  it  easy  and  pleasant  to  write  out  all 
the  moods  and  the  logical  fallacies  by  this  circular  method 


INDIRECT    REDUCTION.  11? 

of  notation  ;  and  as  two  modes  of  coming  at  facts  make  the 
memory  more  tenacious  of  them,  this  practice  will  fix  clearly 
in  his  mind  the  moods  and  figures  of  the  syllogism. 

The  system  also  illustrates  the  categorical  propositions  as 
tc  the  distribution  of  their  terms,  very  satisfactorily  : 


AU  A  is  B, 

No  A  is  B, 
Some  A  is  B, 

Some  A  is  not  B. 

It  would  be  a  good  exercise  for  the  student  to  be  called 
upon  to  represent  any  given  syllogisms  by  this  notation. 


CHAPTER  IX. 

OF  TMREGhLAB,  INFORMAL  AND    COMPOUND  ARGU- 
MENTS. 

(43.)  Of  Abridged  Syllogisms. 

We  have  thus  far  considered  only  those  arguments  which 
appear  directly  and  without  analysis  in  the  form  of  a  simple 
syllogism,  and  have  explained  those  processes  which  we  per 
form  upon  known  and  acknowledged  facts,  stated  as  prem- 
isses and  conclusion ;  but  the  mind  of  man  sometimes  passes 
intuitively  over  certain  steps  of  these  processes  without  stop- 
ping to  express  them,  which  gives  rise  to  abridged  arguments ; 
or  it  halts  in  doubt  and  uncertainty,  being  not  sure  of  its 
facts,  but  frequently  balancing  between  two,  one  of  which 
must  be  true,  because  of  the  truth  or  falsity  of  the  other. 
This  produces  hypothetical  syllogisms. 

All  these  in  the  present  chapter  will  be  treated  of  as  in- 
formal syllogisms,  or  arguments  which  are  not  syllogisms  in 
form,  but  which,  if  they  be  valid,  must  be  capable  of  being 
put  into  the  syllogistic  form. 

The  first  of  the  abridged  arguments  to  be  considered,  be- 
cause the  one  in  most  common  use,  is 

The  Enthymeme.^ 

The  enthymeme  is  a  syllogism  with  one  premiss  suppressed 
it  matters  not  which  ;  thus,  having  the  syllogism  : 

All  men  are  mortal, 
Caesar  is  a  man, 
Csesar  is  mortal, 

*  evOvfieofiac,  to  conceive  in  the  mind. 
118 


OF    ABRIDGED    SYLLOGISMS.  119 

we  may  suppress  the   major  premiss  and  write   the   enthy* 

meme, 

Ceesar  is  a  man. 

Therefore   Caesar  is  mortal. 

Or,  suppressing  the  minor  premiss,  we  have, 

All  men  are  mortal, 
Therefore   Csesar  is  mortal, 

either  of  which  is  a  satisfactory  expression,  became  all  Met 
tenns  of  the  syllogism  are  expressed  in  either  form  of  the  en- 
thymeme,  and  we  can  at  once  reconstruct  the  syllogism  ;  thus, 
taking  the  latter  form,  with  the  minor  premiss  suppressed,  we 
see  by  examining  the  conclusion,  in  which  the  major  and 
minor  terms  are  always  contained,  that  Ccesar  is  the  minor, 
being  the  subject  of  the  conclusion,  and  mortal  the  major, 
being  the  predicate.  3fen,  then,  must  be  the  middle  term, 
and  we  at  once  compare  it  with  the  minor  term  to  form  the 
suppressed  premiss ;  thus, 

Caesar  is  a  man. 
By  a  similar  process  we  may  reconstruct  the  syllogism  when 
the  major  premiss  is  suppressed. 

It  is  worthy  of  observation  that  in  ordinary  discourse  men 
suppress  the  major  premiss  habitually,  as  that  to  which  the 
mind  most  readily  yields  assent,  although,  if  the  proof  of  its 
truth  be  required,  the  task  would  be  more  difficult  than  to 
establish  the  truth  of  the  minor.  Thus,  in  the  example 
givec  above,  we  would  take  for  granted  as  a  fact  that 

All  men  are  mortal ; 
whereas,  without  the  declarations  of  the  Bible — and  Logic, 
as  a  science,  moves  independently  of  any  extraordinary  or 
supernatural  dicta — this  proposition  is  incapable  of  proof; 
for,  although  all  men  have  died  thus  far  in  the  world's  his- 
tory, the  process  of  induction  cannot  be  finished  until  the 
end  of  man  as  a  race. 

But  this  seems  like  a  cavil.     The  major  premiss,  although 


120  LOGIC. 

ihus  incapable  of  mathematical  proof,  is  the  one  which  most 
surely  demands  belief;  and  so,  when  in  the  enthymeme  we 
speak  of  the  suppressed  premiss,  we  mean  the  major  premiJiSy 
unless  it  be  otherwise  explained. 

As  a  simple  rule  for  reconstructing  the  syllogism  from  the 
enthymeme,  we  observe  that, 

If  the  subject  of  the  conclusion  be  found  in  the  expressed 
premiss,  that  premiss  is  the  minor.  If  the  predicate  of  the 
conclusion  be  found  in  the  expressed  premiss,  it  is  the  major. 

Sometimes  it  becomes  necessary  to  put  the  enthymeme  into 
logical  form  before  proceeding  to  reconstruct  it.  Thus,  the 
example  given  above  might  be,  and  most  commonly  is,  thus 
spoken  or  written : 

Caesar  is  mortal, 
Because  Caesar  is  a  man ; 

which  is  evidently  a  transposed  form  of  the  enthymeme. 
Whenever  the  causal  conjunction  because  unites  the  proposi- 
tions of  an  enthymeme,  we  may  invert  the  propositions  and 
unite  them  with  the  illative  conjunction  therefore,  and  then 
proceed  to  reconstruct  the  syllogism  ;  thus, 

Caesar  is  a  man, 
Therefore  He  is  mortal. 

Many  abridged  arguments  which  appear  in  a  hypothetical 
form  are  in  reality  simple  enthymemes  ;  thus. 

If  murder  is  a  crime, 

The  murderer  should  suffer. 

In  which  there  is  really  no  hypothesis  or  condition  in  the 
premiss,  because  all  allow  that  murder  is  a  crime,  and  are 
consequently  ready  to  declare  that 

The  murderer  should  suffer. 

When  the  enthymeme  has  been  reconstructed  into  a  syllogism 
in  any  one  of  the  figures,  we  shall  be  able  to  put  it  directly 
into  the  first  figure,  and  can  then  apply  to  it  the  test  of  Aris- 
totle's dictum. 


THE   SORITES    OR   CHAIN    ARGUMENT. 


12. 


(44.)  The  Sorites*  or  Chain  Argnment.f 
The  Sorites  is  an  abridged  argument  cou.sistiug  of  a  series 
of  propositions  in  which  the  predicate  of  the  first  is  the  subject 
of  the  second,  the  predicate  of  the  second  the  subject  of  the 
third,  and  so  on  until  we  combine  the  subject  of  the  first  and 
the  predicate  of  the  last  to  form  a  conclusion ;  thus, 

A  is  B  ^  The  mind  is  a  thinking  substance. 

B  is  C  =  A  thinking  substance  is  a  spirit. 

C  is  D  =  A  spirit  has  no  composition  of  parts. 

D  is  E  =  (That  which  has)  no  composition  of  parts  is  indissoluble, 

E  is  F  =  (That  which  is)  indissoluble  is  immortal. 

Concl.  A  is  F  =  The  mind  is  immortal. 

This  may  be  illustrated  by  a  figure : 


Now,  if  we  try  to  put  this  collection  of  abridged  arguments 
into  the  syllogistic  form,  in  order  to  apply  the  dictum  of 
Aristotle  to  them,  we  shall  see  that  the  Sorites  is  an  abridg 
ment  of  a  series  of  syllogisms  in  the  first  figure ;  that  the 
term^  B,  C,  D  and  E,  which  are  iLsed  twice,  are  middle  terms, 
and  that  we  may  construct  as  many  syllogisms  as  we  have 
middle  terms.  Taking,  then,  the  second  proposition  of  the 
sorites,  B  is   C,  as  the  major  premiss  of  the  first  syllogism, 

♦  aupeiTTjQ  =z  a  heap,  or  collection. 

t  Called  by  the  Germans,  more  significantly,  Kettenschluss,  or  chain 
argument. 
11 


122  LOGIC. 

and  the  first,  A  is  B,  as  the  minor,  we  shall  have  as  a  concla 
sion  A  is  C,  which  we  use  as  the  minor  premiss  of  a  second 
syllogism,  using  the  third  proposition  of  the  sorites  as  a  major 
premiss ;  and  so  on,  as  long  as  the  middle  terms  last ;  thus, 


l8t. 

2d. 

3d. 

4th. 

BisC, 

CisD, 

DisE, 

EisF, 

AisB, 

AisC, 

AisD, 

AisE, 

AisC. 

AisD. 

AisE. 

AisF. 

A  thinking  substance  is  a  spirit. 
Ist.  The  mind  is  a  thinking  substance. 
The  mind  is  a  spirit. 

A  spirit  has  no  composition  of  parts. 
2d.  The  mind  is  a  spirit. 

The  mind  has  no  composition  of  parts. 

That  which  has  no  composition  of  parts  is  indissoluble. 
3d.  The  mind  has  no  composition  of  parts. 
The  mind  is  indissoluble. 

That  which  is  indissoluble  is  immortal. 
4th.  The  mind  is  indissoluble. 
The  mind  is  immortal. 

These  are  all  in  the  first  figure,  and  consequently  are  forma 
to  which  the  dictum  will  directly  apply. 

It  must  be  observed  that  in  the  sorites  the  first  proposition, 
A  is  B,  is  the  only  one  which  may  be  partieular,  because  it 
is  the  only  minor  premiss  expressed,  every  other  being  used 
as  a  major,  and  we  have  already  seen  that  in  the  first  figure 
the  major  premiss  must  be  universal. 

So,  again,  the  last  proposition,  E  is  F,  is  the  only  one  that 
may  be  negative,  for,  if  any  other  be  negative,  we  should  have 
in  one  of  the  syllogisms  a  negative  conclusion  which  is  to  be 
in  turn  the  minor  premiss  of  the  succeeding  syllogism,  and  we 
have  already  shown  that  in  the  first  figure  the  minor  premiss 
must  be  affirmative.  But  the  conclusion  deduced  from  the 
last  syllogism  does  not  become  a  minor  premiss,  and  so  the 
last  conclusion  may  be  negative ;  it  would  then  read  thus : 


THE   SORITES   OR    CHAIN    ARGUMENT.  123 

No  E  is  F. 
All  A  is  E. 
No  A  is  F. 

Or  the  chain  of  the  sorites  would  be  broken  in  whatever  place 
the  negative  proposition  should  occur. 

The  sorites  is  a  very  simple  and  conclusive  abridged  form 
of  argument ;  for  the  mind,  taking  the  only  expressed  minor 
term  A,  which  is  expressed  in  the  chain,  links  it  by  jumping 
from  middle  term  to  middle  term,  B,  C,  D,  E,  to  the  final 
major  term  or  F,  as  surely  and  more  easily  than  in  the  syllo- 
gisms into  which  it  is  elaborated. 

By  its  aid  we  easily  establish  the  points  in  any  great  argu- 
ment, either  as  recapitulating  the  process  of  the  argument,  or 
as  stating  them  preparatory  to  a  comprehensive  discussion. 
Thus,  to  establish  the  effect  of  a  republican  government,  we 
shall  have — 

The  Americans  make  their  own  laws. 

Those  who  make  their  own  laws  are  free. 

Those  who  are  free  are  contented. 

Those  who  are  contented  are  happy. 
Therefore  The  Americans  are  happy. 

It  is  evident  that  the  sorites  may  be  properly  stated  in  the 
inverse  order,  thus : 

D  is  E,        C  is  D,        B  is  C,        A  is  B, 

Therefore  A  is  E. 

Here  the  sorites  starts  from  its  widest  terms,  D  and  E,  to 
include  the  narrower  and  more  limited  terms,  C,  B,  au  1 
finally  A. 

This  form  is  called  the  Goclenian  Sorites,  from  the  name  of 
its  originator.  It  serves,  perhaps,  better  to  illustrate  the  fact 
stated  that  only  the  most  extensive  proposition,  which  in  the 
ordinary  form  is  the  last,  and  in  this  the  first,  may  be  nega^ 
live;  which,  as  we  have  seen,  will  give  us  a  negative  conclu- 
Bion,  thus  : 

D  is  not  E,  C  is  D,  B  is  C,         A  is  B, 

Therefore  A  is  not  E. 


1 2^  LOGIC. 

Hypothetical  Sorites. 

If  we  have  a  string  of  conditional  propositions,  such  thai 
the  consequent  of  each  becomes  the  antecedent  of  the  succeed- 
ing one,  the  argument  is  called  a  hypothetical  sorites,  and  the 
conclusion  is  obtained  either  by  affirming  the  first  antecedent 
with  the  last  consequent,  or  by  denying  the  last  consequent 
with  the  first  antecedent,  thus : 

1.  If  A  is  B,  C  is  D ;  If  0  is  D,  E  is  F ; 
But  AisB,  Therefore  E  is  F. 

2.  If  A  is  B,  C  is  D ;  If  C  is  D,  E  is  F ; 
But  E  is  not  F,        Therefore  A  is  not  B. 

Examples. 

1. 

If  the  Bible  is  from  God,  it  should  be  taught ; 

If  it  should  be  taught,  men  should  be  set  apart  to  teach ; 

If  men  should  be  set  apart  to  teach,  they  should  be  supported  ; 

But  the  Bible  is  from  God,  therefore  its  teachers  should  be  supported. 

2. 

If  the  Bible  is  false,  it  deceives  the  world ; 

If  it  deceives  the  world,  it  should  be  destroyed ; 

But  it  should  not  be  destroyed,  therefore  it  is  not  false. 

To  the  hypothetical  sorites  it  is  evident  that  the  Goclenian 
form  will  also  apply.  Indeed,  this  is  illustrated  in  the  last 
case  mentioned,  where  we  reason  back  from  the  denial  of  the 
last  consequent  to  the  denial  of  the  first  antecedent. 

(45.)  Of  the  Epichirema.* 

Most  arguments  employed  in  ordinary  conversation  and 

writing  consist  of  simple   syllogisms,  abridged   into   enthy- 

memes,  linked  together  in  a  compound  form  ;  but  in  many  cases 

the  form  of  the  syllogism  is  observed  where  the  premisses  are 

*  The  Greeks  seem  to  have  considered  this  a  great  logical  weapon, 
as  the  name  they  gave  it  signifies  a  violent  onset  or  laying  of  hands  vpon 
tTTL,  and  xtip. 


OF   THE    EPICHIREMA.  12-^ 

arguments  in  themselves.  When  the  premisses  are  thus  sepa 
rately  established,  before  the  conclusion  is  deduced,  the  argu- 
ment is  called  an  Epichirema,  thus : 

The  victors  are  injured  by  war,  because  it  kaidem  their  hearts; 
The  French  icere  victors  at  Marengo,  for  they  retained  the  /ield; 
The  French  were  injured  by  their  victory. 

The  major  premiss  is  an  enthymeme,  which  may  be  ex- 
panded into  a  syllogism  ;  the  same  is  true  of  the  minor ;  hence 
we  have  two  distinct  arguments  within  the  one  which  origi- 
nally appeared.  To  apply  the  tests  to  their  validity,  they 
need  only  be  written  out  in  syllogistic  form.  In  most  ap- 
parently simple  syllogisms  there  is  in  reality  implied  the 
epichirema.  As  for  example,  in  the  one  given  to  illustrate 
the  mood  Fakoro,  of  the  second  figure, 

All  true  patriots  are  friends  to  religion, 

Some  great  statesmen  are  not  friends  to  religion, 

Some  great  statesmen  are  not  true  patriots, 

the  major  premiss  demands  in  itself  a  reason,  thus : 

All  true  patriots  are  friends  to  religion,  because  religion  is  the  basis  of 
national  prosperity  and  advancement. 

So  also  does  the  minor, 

Some  great  statesmen  are  not  friends  to  religion,  because  their  own  lives 
are  not  in  accordance  with  its  precepts. 

Each  of  the  premisses  given  is  an  enthymeme ;  of  w^hich 
the  clause  because,  etc.  is  the  premiss,  and  the  first  statement, 
all  true  patriots,  etc.,  is  the  conclusion.  Now,  this  premisi 
to  the  premiss  is  called  the  prosyllogism. 

Sometimes  the  establishment  of  the  final  conclusion  will 
warrant  us  in  drawing  other  conclusions  also,  thus : 

A  is  B, 
Cis  A, 

Therefore  C  is  B, 
Therefore  X  is  Y,  etc 

n  • 


1 26  LOGIC. 

This  conclusion  from  a  conclusion  (X  is  Y)  is  called  the  epv 
syllogism. 

In  mathematics  it  is  called  a  corollary,  or  something  that 
flows  from  the  demonstration  without  new  proof. 

To  take  the  example  before  quoted,  we  shall  have : 

All  true  'patriots  are  friends  to  religion. 
Some  great  statesmen  are  not  friends  to  religion. 
Some  great  statesmen  are  not  true  patriots. 
Therefore  They  deceive  their  countrymen, 

and  Deserve  no  rewards  from  their  country,  etc. 

A  number  of  syllogisms  joined  together  in  a  connected 
argument  constitutes  a  Poly-syllogism. 

(46.)  Of  Hypothetical  Syllogisms. 
Corresponding  to  the  various  forms  of  hypothetical  proposi- 
tions— viz.,  conditional,  causal,  disjunctive,  etc. — we  have  con- 
ditional, disjunctive  and  causal  syllogisms.  They  are  all  of  so 
simple  a  nature  that  the  mind  finds  no  difficulty  in  the  ratio- 
cination which  they  express ;  but  as  we  have  asserted  that,  if 
valid,  they  may  be  reduced  to  the  form  of  a  categorical  syllo- 
gism in  the  first  figure,  we  proceed  to  show  how  this  may  be 
done. 

Conditional  Syllogisms. 

If  we  examine  a  conditional  proposition,  we  shall  see  at  once 
that  the  affirmation  of  the  co7isequent  will  follow  from  the 
affirmation  of  the  antecedent ;  thus  : 

\i  Kis'R,  Q  isT>  ^=  If  he  has  a  fever,  he  is  sick. 

But  if  we  deny  the  antecedent,  we  may  not  therefore  deny  the 
consequent,  since  this  consequent  might  spring  from  some 
other  antecedent  as  well  as  from  the  one  given,  thus : 

If  A  is  not  B  =  if  he  ha^  not  a  fever, 

we  cannot  say, 

C  is  not  D  ^^  he  is  not  sick, 
Since 


OP    HYPOTHETICAL   SYLLOGISMS.  127 

C  might  be  I)  -=  he  might  be  sick, 
from  some  other  cause  than 

A  being  B,  or  his  having  a  fever. 

For  similar  reasons  we  may  pass  from  the  denial  of  the 
consequent  to  the  denial  of  the  antecedent,  but  not  from  the 
affirmation  of  the  consequent  to  the  affirmation  of  the  antecedent. 
Wlien  we  pass  from  the  affirmation  of  ths  antecedent  to  the 
affirmation  of  the  consequent,  the  reasoning  is  called  constructive ; 
and  when  we  pass  from  the  denial  of  the  consequent  to  the 
denial  of  the  antecedent,  it  is  called  destructive. 

We  may  have,  then,  two,  and  only  two,  forms  of  conditional 
syllogisms,  constructive  and  destructive.  To  form  the  first,  we 
take  the  whole  conditional  proposition  as  the  major  premiss ; 
the  affirmation  of  the  antecedent  for  the  minor,  from  which 
premisses  we  shall  draw  the  affirmation  of  the  consequent  as 
the  conclusion,  thus : 

Maj.  prem.     If  A  is  B,  C  is  D  =  If  he  has  a  fever,  he  is  sick. 
Min.  prem.     A  is  B  =:  He  has  a  fever. 

Conclusion.    C  is  D  =  He  is  sick. 

To  frame  the  desti^ctive  conditional  syllogism,  we  take  the 
whole  proposition  as  before  for  a  major  premiss,  the  denial  of 
the  consequent  for  a  minor,  and  we  deduce  as  a  conclusion  the 
denial  of  the  antecedent,  thus  : 

^faj.  prem.     If  A  is  B,  C  is  D  =  If  he  has  a  fever,  he  is  sick. 
Min.  prem.     C  is  not  D  =  He  is  not  sick. 

Conclusion.    A  is  not  B  =  He  has  not  a  fever. 

As  these  are  the  only  possible  forms  of  conditional  syllo- 
^ms,  and  as  we  have  shown  that  all  other  forms  of  hypo- 
thetical propositions — disjunctive,  causal,  etc. — may  be  easily 
reduced  to  conditional  propositions,  we  have  only  to  show  how 
these  conditional  syllogisms  may  be  reduced  to  the  form  of 
simple  categorical  syllogisms,  and  we  shall,  in  effect,  have 
shown  it  for  all. 

Considering  first  the  constructive  form,  and  remembering 


128  LOGIC. 

that  the  form  of  condition  may  be  removed  by  the  phrases 
^Hhe  case  of  and  "the  present  case,"  and  that  the  proposition 
assumes  the  form  of  a  categorical  proposition,  of  which  the 
antecedent  becomes  the  subject,  and  the  consequent  becomes  a 
predicate,  we  shall  have  for  the  constructive  form, 

X  Y 


Maj.  pjem.     The  case  of  A  being  B     is     the  case  of  C  being  D 
Z  X 


Min.  prem.     The  present  case    is    the  case  of  A  being  B. 
Z  Y 


Cond.  The  present  case    is    the  case  of  C  being  D. 

Or,  All  X  is  Y.  (A) 
All  Z  is  X.  (A) 
All  Z  is  Y.     (A) 

which,  X  being  the  middle  term,  is  evidently  in  the  first 

figure,  and  the  dictum  may  be  at  once  applied.     Using  the 

same  phraseology,  and  thus  translating  the  destructive  form, 

we  have, 

X  Y 


The  case  of  A  being  B    is    the  case  of  C  being  D. 
Z  Y 


The  present  case    is  not    the  case  of  C  being  D. 
Z  X 


The  present  case    is  not    the  case  of  A  being  B. 

Or,  All  X  is  Y.     (A) 

No  Z  is  Y.     (E) 
No  Z  is  X.     (E) 

which,  Y  being  the  middle  term,  is  in  the  second  figure,  and 
in  the  mood  Camestres,  which  must  be  reduced  to  the  first 
figure  or  the  form  of  the  dictum. 

If,  now,  we  perform  the  operations  indicated  to  reduce  this 
mood  {m,  s,  s),  we  simplv  convert  the  minor  premiss,  and  ther 


OF    HYPOTHETICAL   SYLLOGISMS.  1 29 

transpose  the  premisses,  and  simply  convert  the  conciusior 

we  shall  have, 

Y  Z 


The  ca.se  of  C  being  I )         is  not         the  present  case. 
X  Y 


The  case  of  A  being  B        is         the  case  of  C  being  D. 
X  Z 


The  case  of  A  being  B        is  not        the  present  case. 
or  simply  converting  the  conclusion, 


The  present  case  is  not  the  case  of  A  being  B. 

No  Y  is  Z.  (E) 
All  X  is  Y.  (A) 
NoXisZ.   (E) 

or,      No  Z  is  X. 

which  is  the  form  of  Celarent  in  the  first  figure. 

The  logical  form  of  the  conditional  does  not  depend  upon 
the  subject-matter  of  the  propositions  composing  it.  There 
may  be,  for  example,  two  apparently  independent  proposi- 
tions— that  is,  propositions  in  which  the  terms  are  entirely 
distinct — thus  conjoined,  or  there  may  be  a  term  the  same  in 
each,  which  will  cause  no  difference  in  the  logical  form  ;  thus 
we  may  have — 

If  A  is  B,  C  is  D  =  If  John  remain,  James  will  go ;  or. 
If  A  is  B,  A  L"!  C  =  If  the  Bible  is  true,  it  (the  Bible)  deserves  oui 
attention. 

To  explain  this  apparent  difference,  it  will  be  remembered 
that  A,  B,  C,  etc.,  although  terms  in  the  proposition,  are  not 
the  terms  of  the  syllogism  when  it  is  put  in  a  categorical 
form,  but  that  the  antecedent  and  consequent  become  the  true 
tenns ;  and  therefore  it  matters  not  whether  there  be  three  or 
Jour  independent  terms  in  the  conditional  proposition  before 

its  change  of  form. 

1 


130  LOGIC. 

A  few  examples  of  conditional  syllogisms  are  given  tc 
accustom  the  student  to  the  form,  and  to  guard  him  against 
the  improper  use  of  it. 

Examples. 

1. 
If  the  fourth  commandment  is  obligatory  upon  us,  we  are  bourd  to 
get  apart  one  day  in  seven. 

But  the  fourth  commandment  is  obligatory  upon  us. 
Therefore  we  are  bound  to  set  apart,  etc. 

2. 

If  any  theory  could  be  framed  to  explain  the  establishment  of  Chris- 
tianity by  human  causes,  such  a  theory  would  have  been  proposed 
before  now. 

But  none  has  been  proposed. 

Therefore  no  such  can  be  framed. 

3. 

If  the  eclipses  of  Jupiter's  moons  occur  sixteen  minutes  later,  when 
the  earth  is  farthest  from  Jupiter,  than  when  she  is  nearest  to  Jupiter 
light  must  travel  ninety-five  millions  of  miles  in  eight  minutes. 

But  these  eclipses  do  occur  so  much  later  in  the  given  positioi^. 

Therefore  light  travels  at  the  rate  stated,  or,  two  hundred  thousand 
miles  in  a  second. 

4. 

If  taste  is  uniform,  all  men  will  admire  the  same  objects. 

But  all  men  do  not  admire  the  same  objects  (one  sees  beauty  where 
another  only  finds  deformity). 

Therefore  taste  is  not  uniform. 

Disjunctive  Syllogisms. 
A  disjunctive  syllogism  is  one  the  major  premiss  of  which 
is  a  disjunctive  proposition  (26),  and  the  minor  a  categorical. 

Brutus  was  either  a  parricide  or  a  patriot  =  Either  A  is  B,  or  it  is  C. 
He  was  not  a  parricide  =  A  is  not  B. 

He  was  a  patriot  =  A  is  C. 

Here,  when  the  major  premiss  consists  of  two  members 
only,  the  minor  asserts  the  one  and  the  conclusion  denies  the 
other ;  or,  the  ?  linor  denies  the  one  and  the  conclusion  assert* 


OF    HYPOTHKTICAL   SYLLOGISMS.  131 

th»     jthei.     Or   we  may   have,  instead    of  two   alLernativea, 
*hree  or  more,  thus  : 

Th6  ttngle  A  must  be  equal  to,  or  greater  or  less  than,  the  angle  B. 
Ikit  it  IS  neither  greater  nor  less  than  it. 
Therefore  it  is  equal  to  it. 

It  is  evideut  that  the  disjunctive  syllogism  may  be  at  once 
stated  in  a  categorical  form  by  any  simple  phraseology  which 
will  rid  us  of  che  disjunctive  form,  thus: 

Brutus  could  dot  be  at  the  same  time  a  parricide  and  a  patriot  (but 
must  be  one  of  the  two). 
He  was  a  patriot, 
Therefore  he  was  not  a  parricide. 
Or,  He  was  not  a  parricide, 
Therefore  he  was  a  patriot. 

Examples  of  Disjurictive  Syllogisms. 

1. 
It  is  either  true  that  knowledge  is  useful,  or  that  ignorance  is  so. 
But  it  is  not  true  that  ignorance  is  useful. 
Therefore  knowledge  is  so. 

2. 
Mohammed  was  either  an  enthusiast  or  an  impostor. 
He  was  an  enthusiast. 
Therefore  he  was  not  an  impostor. 

This  is  Gibbon's  argument,  but  it  is  faulty  in  point  of  fact, 
for  a  man  may  be  both  enthusiast  and  impostor,  and  some 
men  have  a  great  enthusiasm  for  imposture. 

3. 
A  government  either  license.-  a  free  press,  or  it  is  oppressive. 
The  French  government  does  not  license  a  free  press. 
Therefore  it  is  oppressive. 

4. 

A  wise  lawgiver  must  either  recognize  future  rewards  and  p  niish' 

ments,  or  mu.st  appeal  to  an  extraordinary  Providence. 
Moses  did  not  do  the  former. 
Therefore  he  must  have  done  the  latter. 


132 


LOGIC. 


0/  the  Dilemma,  Trilemma,  etc.* 
A  dilemma  is  a  compound  argument  composed  of  condv 
tional  propositions  upon  which  we  reason  disjunctively. 
When  two  conditional  propositions  are  combined  with  a  dis- 
junctive minor  premiss,  the  argument  is  called  a  dilemma. 
When  three,  four,  etc.  are  so  combined,  they  constitute  a 
trilemma  tessaralemma,  etc.  The  generic  name  Dilemma, 
however,  is  technically  given  to  them  all.  Dilemmas  are 
divided  into  four  kinds,  according  to  their  being  simple  or 
complex,  constructive  or  destructive. 

A  simple  dilemma  is  one  in  which  we  have  as  a  major  pre- 
miss several  antecedents  with  a  single  consequent,  thus : 


Maj,  prem. 


If  A  is  B, 
,  XX  C  is  D,  then  X  is  Y, 
I  If  E  is  F. 


r 


Min,  prem.   ■{ 


Conclusion.    Therefore  X  is  Y, 


'  But  either 
AisB 

or 
CisD 

or 
EisF 


A  complex  dilemma  is  one  in  which  we  have  several  ante- 
cedents, and  each  has  its  own  consequent,  thus : 


Maj.  prem.  - 


If  A  is  B,  G  is  H. 
If  C  is  D,  I  is  K. 
If  E  is  F,  L  is  M. 


Oondusion.    Therefore 


Min.  prem.   - 


Either 
GisH 

or 
lisK 

or 
LisM 


Either 
AisB 

or 
CisD 

or 
EisF 


Now,  if  in  the  simple  dilemma,  instead  of  reasoning  as  we 
have  done  constructively  from  the  disjunctive  affirmation  of  the 
*  di( ;  rpeic,  TEcaape^,  etc.,  and  ^/j/ua,  from  Xafiftavu. 


OF    HYPOTHETICAL   SYLLOGISMS.  132 

antecedents  to  the  disjunctive  affirmation  of  the  consequent,  we 
reason  destructively — that  is,  deny  the  single  consequent — then 
all  the  antecedents  fall  to  the  ground  ;  there  is  no  longer  the 
condition  of  the  dilemma ;  for  we  have  a  simple  conditional 
syllogism.  Or  if  we  have  one  antecedent  and  several  conse- 
quents, and  reason  destructively,  it  is  as  though  we  had  but  one 
wnsequent,  since  the  denial  of  any  one  requires  the  denial  of 
the  one  antecedent;  thus,  in  the  argument, 


isD, 
If  A  is  B,     \G  is  H, 
[lIsM, 


\i 


it  matters  not  whether  we  deny  one  or  all  the  consequents,  the 
denial  of  the  antecedent  follows.  Hence,  properly  speaking, 
there  is  no  such  thing  as  a  simple  destructive  dilemma.  It  dif- 
fers in  no  wise  from  a  simple  destructive  conditional  syllo- 
gism. 

The  destructive  dilemma  proper,  then,  consists  of  several 
antecedents,  each  with  its  own  consequent,  in  which  we  disjunc- 
tively deny  the  consequents — that  is,  deny  any  of  them  or  all  in 
turn — and  we  may  disjunctively  deny  the  antecedents. 

_^  .  If  A  Ls  B,   C  is  D.  „  But  either  C  is  not  D 

Mat.  mem.  ^c  r>  -    tt   t  •   ht  Mm.  previ.  t  •        ^  ■»*• 

*'  ^  If  Gr  IS  H,  L 13  M.  ^  or         L  is  not  M. 

etc.  etc. 

Conclusion.     Therefore  either  A  is  not  B, 

or     G  is  not  H. 

To  apply  this  abstract  form  to  a  particular  example ;  let  ua 
take  the  argument  of  Antisthenes  : 

If  we  conduct  the  affairs  of  state  well,  we  offend  men 
J.  yr     .  j^  ^^  conduct  them  ill,  we  offend  the  gods. 

If  now  we  reason  constructively  we  shall  add. 

But,  we  must  either  conduct  them  well, 
'P       '  or  conduct  them  ill. 

Concli  sion.     Therefore  we  must  either  offend  men, 
or  offend  the  gods. 
13 


134  LOGIC. 

If  we  reason  destructively,  we  add,  as  a  minor  premiss, 

But  we  must  either  not  offend  men,  or  not  offend  the  gods, 

and  as  a  conclusion, 

Therefore,  we  must  either  not  conduct  them  well,  or  not  conduct 
them  ill. 

To  rid  themselves  of  the  perplexities  of  the  dilemma,  the 
old  logicians  always  established  from  their  premisses  an  un- 
due, because  not  a  logical,  conclusion,  but  a  moral  and  mate- 
rial one,  a  passage  of  the  mind  to  a  purpose  which  had  been 
suggested  by  the  matter  of  the  argument ;  thus,  the  conclu- 
sion of  Antisthenes  from  the  perplexity  of  the  dilemma  was, 
that  we  had  better  not  meddle  with  the  affairs  of  state  at  all. 
Take  another  illustration: 

If  a  wife  is  beautiful,  she  excites  jealousy 
If  she  is  ugly,  she  gives  disgust ; 

and  the  illogical  but  common  conclusion  is 

It  is  best  not  to  marry. 

Most  logicians  have  erred  at  the  very  outset  by  supposing 
that,  because  there  is  an  alternative  expressed  in  the  dilemma, 
it  is  a  disjunctive  instead  of  a  conditional  syllogism,  and  thus 
have  rendered  it  a  vehicre  of  fallacy  which  it  would  be  im- 
possible for  Logic  to  arrest ;  thus,  they  would  read  the  last 
example. 

Either  a  wife  excites  jealousy  by  her  beauty, 

Or  disgust  by  her  ugliness ; 

Hence  it  is  better  not  to  marry. 

In  any  such  case,  if  we  first  put  the  dilemma  in  its  true 
conditional  form,  and  then  (leaving  the  province  of  Logic, 
wnich  presumes  all  given  propositions  to  be  true)  examine 
the  subject-matter  of  the  propositions  themselves,  we  shall  find 
the  falsity  which  causes  perplexity ;  thus,  it  is  not  true  univer- 


J 


HYPOTHETICAL   SYLLOGISMS.  136 


%aU]j,  nor  commonly,  as  is  implied  in  the  example,  that  if  a 
wife  is  beautiful  she  excites  jealousy.  It  is  even  less  true,  that 
is,  in  a  fewer  number  of  cases,  that  if  she  is  ugly  she  causes 
disgust;  hence  the  conclusion  that  it  is  best  not  to  marry  is 
less  true,  i.  e.,  applies  to  a  fewer  number  of  cases,  than  either 
of  the  foregoing  assertions,  i.  e.,  the  falsehood  is  increased  by 
the  number  of  false  statements  preceding  the  conclusion. 

It  is  evident  that  the  dilemma  may  be  resolved  into  as 
many  conditional  syllogisms  as  the  greatest  number  of  ante- 
cedents or  consequents,  and  that  these  may  be  reduced  ac- 
cording to  the  rules  for  the  reduction  of  conditional  syllo- 
gisms. 

Any  dilemma  may  also  be  stated  in  a  categorical  form. 

Thus, 

The  case  of  A  being  B,  is  the  case  of  G  being  H, 
The  case  of  C  being  D,  is  the  case  of  E  being  F ; 

and  we  may  then  proceed  as  in  conditional  syllogisms. 

Examples  of  the  Dilemma. 
1. 
If  Eschines  joined  in  the  public  rejoicings,  he  was  inconsistent. 
If  he  did  not,  he  was  unpatriotic. 
But  either  he  did  join,  or  he  did  not. 
Therefore,  he  was  either  inconsistent  or  unpatriotic. 

The  following  dilemma  was  formed  to  confute  the  doctrine 
of  Pyrrho,  the  skeptic,  which  was,  that  because  everything 
has  its  contradictory,  everything  \s  false;  or  that  no  one  could 
know  anything  certainly : 

2. 

If  what  you  say  is  true,  then  there  is  something  which  is  not  fal«»e; 
ergo,  your  system  is  wrong. 

If  what  you  say  is  false,  then  it  has  no  value  as  an  argument  ;  i.  «^ 
vour  system  is  wrong. 

But  what  you  say  must  be  either  true  or  false. 

Therefore,  in  either  case  your  system  is  wrong. 


136 


LOGIC. 


3. 

There  are  two  kinds  of  things  which  we  ought  n  :>t  to  fret  about— 
what  we  can  help  and  what  we  cannot. 

(The  student  will  put  this  in  the  form  of  a  dilemma.) 

Having  explained  the  various  forms  of  argument,  simple 
and  compound,  our  next  subject  of  investigation  is  of  the 
erroneous  use  of  these  forms.  To  this  has  be^^given  the 
generic  title  of  Fallacies. 


CHAPTER   X. 

^'  FALLACIES. 

(47.)  Trfr  Meaning  and  Comprehension  of  a  Fallacy." 
DifJRient  terms  are  used  to  express  the  errors  which  are 
fouD^ft  ^enrw,  propositions  or  argument  in  Logic.  Thus,  we 
^flf  a  ^erm,  when  it  is  not  uni-vocal,  i.  e.,  when  it  has  not 
olRneaning  and  only  one,  that  it  is  equivocal  or  ambiguous, 
I.  e.,  has  more  than  one  meaning  ;  of  a  proposition,  if  it  be  not 
true,  that  it  is  fake,  which  expresses  in  other  words  that  the 
predicate  and  subject  have  no  proper  connection ;  of  an  argvr 
merit  we  say,  when  it  violates  the  dictum  of  Aristotle  or  any 
of  the  rules  given,  that  it  is  invalid,  and  sometimes  of  an  in- 
valid argument  we  say  that  it  is  fallacious. 

A  fallacy,  then,  is  an  invalid  argument  ivhich  appears  ai  first 
sight  to  be  valid.  If  it  be  used  with  the  intention  to  deceive,  the 
fallacy  is  called  a  sophism.-f  An  argument  manifestly  and 
foolishly  invalid  would  then  be  neither  a  sophism  nor  a  fal- 
lacy. 

The  subject  of  fallacies  is  one  of  the  most  important  in  the 
study  of  Logic,  for  not  only  is  Logic  designed  to  teach  us  to 
reason  correctly,  but  also  it  should  teach  us  to  perceive  and 
detect  all  errors  in  reasoning.  Hence  we  find  the  earliest 
writers  on  Logic  giving  rules  and  cautions  for  avoiding  and 
detecting  fallacies. 

The  first  division  of  fallacies  which  they  have  made  is  into 

*  Folio  =  to  deceive. 

t  Sophism  comes  through  the  word  ^(piarric,  from  ao^f,  v;we.  Sophist 
wiis  the  name  given  in  irony  to  the«€  whose  loisdom  showed  itse'f  in  ar 
almse  of  words  and  reasoning. 

12*  137 


138  LOGIC. 

fallacies  in  dieticne  and  extra  dictionem.  As  diclio  means 
the  form  of  words,  and  not  the  meaning  of  the  words,  or 
what  is  expressed  in  our  word  diction,  the  class  in  dictione, 
or  fallacies  in  form,  will  evidently  come  within  the  province 
of  Logic,  while  those  extra  dictionem,  not  being  in  the  form, 
but  in  the  subject-matter,  with  which  Logic  is  only  indirectly 
concerned,  will  really  not  fall  within  the  scope  of  our  study. 
But  since  the  line  between  the  two,  although  easy  to  be 
drawn,  is  continually  mistaken  in  practical  argument  or  con- 
troversy unless  it  be  thus  drawn,  it  becomes  necessary  to 
explain  both  classes  with  care,  that  we  may  always  distinguish 
between  the  truly  Logical  and  the  non-Logical  or  material 
fallacies;  and  this  is  particularly  important,  because  those 
who  resort  to  fallacious  reasoning  use  both  these  kinds  of 
fallacy  in.  combination  with  each  other.  One  class  of  these 
material  fallacies,  which  arises  from  the  ambiguity  in  words, 
and  is  therefore  called  verbal  fallacies,  needs  but  a  slight 
change,  as  we  shall  see,  to  become  formal  or  logical  fallacies. 

(48.)  Of  Fallacies  in  Dictione,  or  Formal  Fallacies. 

These  are  the  fallacies  about  which  Logic  is  particularly 
concerned. 

Under  this  class  are  included  all  violations  of  the  dic- 
tum of  Aristotle,  and  of  the  axioms  and  rules  laid  down  for 
determining  the  validity  of  an  argument.  The  fallacy  in 
all  cases  under  this  head  is  apparent  in  the  form  of  the  ex- 
pression ;  hence  the  name  formal  fallacies.     Of  this  kind  are — 

1  Undistributed  middle  terms. 

2  Illicit  process  of  either  term. 

3.  Negative  premisses. 

4.  Affirmative  conclusion  from  a  negative  premiss,  and 
trice  versa. 

5.  More  than  three  terms  in  the  argument. 

Of  these,  repeated  examples  have  been  already  given  in 


OF  FALLACIES  IN  DICTIONE,  OR  FORMAL  FALLACIES.    139 

syllogistic  form  ;  it  is  only  by  putting  them  in  this  form  that 
the  fallacy  is  at  once  and  easily  detected. 

But  it  should  be  borne  in  mind  that  in  practice  such  falla- 
cies are  not  stated  in  the  syllogistic  form,  in  which  they  are 
thus  easily  to  be  detected,  but  are  stated  in  the  form  of  an 
enthymeme,  or  other  abridged  argument,  and  so  covered  with 
words  that  the  effect  is  produced  without  the  mind  being  con- 
vinced— the  conclusion  allowed,  because  the  mind  cannot  see 
the  false  steps  which  have  been  used,  although  it  has  not  cer- 
tified itself  that  the  true  have  been  taken.  Let  the  student 
then  take  the  trouble,  in  each  such  case,  to  write  out  the 
argument  in  syllogistic  form,  and,  for  greater  clearness,  to  use 
symbols,  and  the  invalidity  will  be  apparent. 

Thus,  we  are  told  that  "  a  certain  man  was  a  good  father, 
because  he  attended  to  the  physical  necessities  of  his  chil- 
dren ;"  food  and  clothing  and  shelter  being  the  criterion  of  a 
good  father.  Let  us  apply  the  test  of  Logic  to  such  an 
argument : 


All  good  fathers  provide  for  the  physical  wants  of 

^^«^-  P''^'  their  children. 


Min.  prem.     A  B         did  thus  provide 
Z  X 


Therefore    A  B        was  a  good  father. 

Or,  using  symbols, 

AllXisY, 

ZisY, 

ZisX. 

That  is,  Y,  which  is  the  middle  term,  is  undistributed,  be.ng 
the  predicate  in  two  affirmative  premisses. 

Again,  it  is  asserted  that  "  brutes  are  not  accountable  beings, 
because  they  are  not  responsible;"  which  involves  a  fallacy 
-)f  illicit  process.     Thus, 


140  LOGIC. 

X 


Maj.  prem.     All  responsible  beings       are       accountable. 
Z  X 


Min.  prem.     Brutes        are  not        responsible  beings. 
Z  Y 


Therefore     Brutes         are  not         accountable. 

AllXis  Y, 
No  ZisX, 
No    ZisY. 

In  which  Y,  which  is  distributed  in  the  conclusion — being 
the  predicate  of  a  negative  proposition — is  undistributed  in 
the  major  premiss :  an  illicit  process  of  the  major  term. 

It  will  be  observed,  in  this  latter  instance,  that  the  conclu- 
fion  is,  we  believe,  a  true  one,  but  it  is  not  reached  by  such 
premisses ;  and  thus  indeed  it  constantly  happens,  that  men 
adopt  a  conclusion  on  internal  grounds  which  they  cannot 
explain,  and  then  seek  in  every  direction  for  premisses  by 
which  to  substantiate  it :  and  so,  on  the  other  hand,  many  a 
just  statement  loses  credence,  from  the  fact  that  weak  and 
empirical  men  undertake  to  prove  it  by  false  premisses  or 
fallacious  reasoning. 

It  is  further  to  be  remarked  that  men  who  are  guilty  of 
fallacy  in  argument,  either  through  design  to  deceive  or 
weakness  of  reasoning  power,  are  apt  to  combine  many  single 
arguments  into  a  compound  argument.  If,  then,  one  of  these 
be  faulty  in  its  ratiocination,  every  ulterior  conclusion  is  en- 
dangered, and  the  whole  chain  of  argument  is  fallacious.  To 
detect  the  error,  therefore,  requires  that  the  whole  chain  be 
exposed  link  by  link,  and  that  the  proper  tests  be  applied  to 
each  argument.  We  have  given  examples  of  the  fallacy  of 
undistributed  middle  and  illicit  2orocess;  the  student  will  not 
need  illustrations  of  the  other  formal  fallacies  mentioned. 


MATERIAL,    OR    INFORMAL    FALLACIES.  141 

(49.)  Material,  or  Informal  Fallacies. 

It  wilJ  be  allowed  that  in  every  fallacious  argument  the 
conclusion  does  or  does  not  follow  from  the  premisses.  If  it  do 
not  follow  from  the  premisses,  then  when  written  out  by  sym- 
bols the  fallacy  is  apparent,  coming  under  one  of  the  heads 
of  formal  fallacies  which  we  have  just  enumerated.  The  fault 
here  is  evidently  in  the  reasoning ;  but  when  the  conclusion 
does  follow  from  the  premisses,  when  written  out  by  symbols, 
the  fallacy  is  not  apparent,  the  fault  will  not  lie  in  the  reason- 
ing, but  either  in  the  premisses  or  in  the  conclusion,  i.  e.,  as  to 
their  t)^th  or  falsity,  or  as  to  the  ambiguous  meaning  of  words 
used  in  both.  Such  fallacies,  with  which  Logic  is  not  directly 
concerned,  are  called  Material  Fallacies. 

It  has  been  remarked  before  that  Logic  indeed  takes  for 
granted  that  the  propositions  composing  its  syllogisms  are 
true,  and  that,  when  we  write  the  general  proposition  A  is  B, 
no  meanings  shall  be  given  to  A  and  B  which  shall  violate 
the  truth  of  the  proposition.  If  then  we  put  for  A,  Learn- 
ing, and  for  B,  useless,  and  thus  write. 

Learning  is  useless, 

or,  by  a  change  of  words,  the  doctrine  of  the  Stoics, 
Pain  is  (a  lesser  sort  of)  pleasure, 

we  shall  reason  to  false  conclusions,  the  matter  of  the  prop- 
ositions forming  the  syllogism  being  false,  while  the  logic  of  the 
argument  may  be  correct.  It  must  be  allowed  that  material 
fallacies  are  more  numerous  and  more  fruitful  causes  of 
error  than  the  logical,  and  as  such  deserve  a  special  consid- 
eration, although  indirectly  allied  to  our  subject. 

We  shall,  therefore,  endeavor  briefly  to  give  the  principal 
forms  or  titles  of  material  fallacies,  and  to  illustrate  them  by 
examples,  observing,  at  the  outset,  that  they  assume  many  and 
varied  forms  under  these  titles,  all  of  which  we  cannot  take 
the  time  to  consider. 


142  LOGIC. 

The  simplest  division  of  them  is  one  which  grows  oat  of 
the  consideration  of — 

1.  Errors  in  the  premisses. 

2.  Drrors  in  the  conclusion. 

Of  Errors  in  the  Premisses. 

Logicians  have  adopted  technical  names  for  the  fallacies 
of  this  kind,  viz. :  the  peiitio  principii,  or  begging  the  questiori: 
Arguing  in  a  circle;  Non  causa  pro  causa,  or  the  assignment 
of  a  false  or  undue  cause.  These  branch  out  into  various 
minor  divisions. 

As  all  these  grow  out  of  a  false  or  undue  assumption  of 
premisses,  they  are  akin  to  each  other,  and  in  many  cases 
are  not  easily  to  be  distinguished.  Especially  is  this  true  of 
the  first  two. 

I.  Petitio  principii.  This  consists  in  using  as  a  premiss  to 
support  an  adopted  conclusion  or  assertion  the  same  fact  in 
other  words.  Thus  we  are  told  that  "  if  the  heart  be  touched 
death  ensues,  because  it  is  a  vital  part,"  or  that  "  morphia  pro- 
duces sleep  because  it  is  an  anodyne." 

Now  what  is  it  to  say  but  that  death  ensues  when  the 
heart  is  touched,  because  death  doth  ensue  f  or  that  morphia 
produces  sleep  because  it  produces  sleep  f 

Our  language,  which  has  so  many  synonyms  from  the  Anglo- 
Saxon  and  the  Latin,  gives  full  play  to  this  sort  of  fallacy, 
and  many  a  wordy  man  is  guilty  of  it  without  knowing  his 
own  error.  And  besides,  this  fallacy  is  the  just  recompense 
of  those  who  endeavor  to  prove  axioms,  or  who  seek  to  pene- 
trate into  the  ultimate  facts  for  which  God  assigns  no  cause 
but  the  fiat  of  his  own  will. 

IL  Arguing  in  a  circle.  This  fallacy  depends  upon  find- 
ing a  premiss  to  prove  an  asserted  conclusion,  and  then,  when 
asked  for  the  proof  of  the  truth  of  that  premiss,  endeavoring 
to  make  the  conclusion  prove  the  premiss ;  or,  as  this  would 
be  easy  of  detection,  to  make  the  circle  still  larger — i.  e., 


MATERIAL,    OR    INFORMAL    FALLACIES.  143 

proving  the  truth  of  the  premiss  by  a  third  proposition  which 
depends  upon  the  conclusion,  and  the  playing  upon  these 
three,  like  the  juggler's  balls  of  which  one  is  always  in  the 
air,  but  which,  it  is  very  difficult  to  tell.  In  case  of  the 
simplest  form,  writing  out  the  syllogism  will  detect  it;  and 
in  the  latter  and  more  complex  case,  the  sorites,  or  its  syllo- 
gisms written  out,  will  find  it  out. 

Thus,  many  men,  not  content  with  the  everywhere  shining 
proof  within  and  without  that  there  is  a  God,  and  mistaking 
the  relations  which  the  Holy  Scriptures  bear  to  him,  would 
prove  the  existence  of  a  God  from  the  truth  of  the  Scriptures, 
and  then  prove  the  inspiration  of  the  Scriptures  from  the  fact 
that  they  came  from  God. 

Ai^  the  Scriptures  are  the  word  of  Ood,  what  they  declare  must  he  true. 
The  Scriptures  declare  that  God  exists. 
Therefore  That  God  exists  is  true. 


Or  again : 


The  uord  of  God  must  he  true. 

The  Scriptures  are  the  word  of  God. 

The  Scriptures  are  true. 


III.  No7i  causa  pro  causa.  This  fallacy,  which  indeed 
may  stand  for  the  general  title  of  unduly  assumed  premisses, 
consists  technically  in  assigning  as  a  reason  or  cause  in  the 
premisses  one  which  has  nothing  to  do  with  the  conclusion, 
or  one  which  is  not  itself  proven,  and  is  not  therefore  a  suf 
ficient  cause.  The  first  of  these  errors  is  called  the  fallacy 
of  a  non  tali  causa  pro  tali,  or  the  assignment  of  a  cause  as 
though  it  were  a  cause,  when  it  is  not ;  and  the  second  is  the 
1  ncKi  vera  pro  vera,  in  which  the  assumed  premiss  cannot  be 
proven  to  be  true  as  a  cause,  and  may  therefore  be  consid- 
ered false.  Under  this  head  we  have  the  fallacies  technically 
called  post  hoc  ergo  propter  hoc,  or  considering  an  event  as  a 
cause,  because  it  precedes  another  event,  and  eiim  hoc  ergo 
propter  hoc,  taking  something  for  a  cause  when  it  occura 
simultaneously  with  an  event. 


1 44  LOGIC. 

Of  the  latter  of  these  divisions,  the  a  non  vera,  we  find  a 
striking  example,  and  an  excellent  logical  retort,  in  the 
reported  dialogue  between  Charles  II.  and  Milton,  after  the 
poet  had  become  blind.  "  Think  you  not,"  said  the  king, 
"  that  the  crime  which  you  committed  against  my  father  must 
have  been  very  great,  seeing  that  Heaven  has  seen  fit  to  pun- 
ish it  by  such  a  severe  loss  as  that  which  you  have  sustained  ?" 
"Nay,  sire,"  Milton  replied,  "  if  my  crime  on  that  account  be 
adjudged  great,  how  much  greater  must  have  been  the  crimi- 
nality of  your  father,  seeing  that  I  have  only  lost  my  eyes, 
but  he  his  head !"  Another  and  common  example  of  this  is 
the  following : 

The  natives  of  barbarous  countries  regard  an  eclipse  as 
portentous  of  war  and  famine ;  and  should  they  come  together, 
they  would  assign  it  as  the  cause  of  their  trouble.  We 
know  that  it  is  not,  but  they  only  note  the  conjunction  of  the 
two  as  satisfactory  proof  that  it  is.  Either  of  these  may  be 
easily  written  out  in  the  syllogistic  form,  in  which  the  propo- 
sitions can  be  scrutinized  as  to  their  subject-matter  and  the 
falsity  detected. 

The  fallacy  of  a  non  tali  is  chiefly  used  in  analogous  in- 
stances, where  things  which  in  one  connection  are  useful  or 
hurtful  are  assumed  to  be  useful  or  hurtful  in  all ;  as  because 
dry  weather  is  good  for  the  traveler  it  is  also  good  for  the 
farmer,  or  because  the  corn-laws  were  beneficial  to  England 
at  one  time  they  must  always  be  so.     Of  the  a  non  tali,  the 
following  example  will  serve  as  an  illustration,  viz. : 
All  poisons  should  be  avoided. 
Brandy  and  wine  are  poisons. 
Therefore  They  should  be  avoided. 

That  is,  they  are  poisons  only  when  taken  in  certain  amounts 
and  under  certain  circumstances.  This  is  an  invalid  argu- 
ment used  by  many  good  persons,  the  true  reason  for  avoid- 
ing brandy  and  wine  being  the  danger  of  acquiring  a  habit 
of  using  them  to  such  an  extent  that  they  will  be  poisons. 


MATERIAL,    OR    INFORMAL    FALLACIRS.  140 

Enrrors  in  the  Conclusion. 

We  come  now  to  the  second  division  of  material  fallacies — 
those  in  which  the  error  lies  in  the  conclusion ;  they  are  all 
included  under  the  general  head  of  Ignoratio  elenchi,  or  irrel 
evant  co7iclusion. 

The  word  elenchus,  as  used  in  the  early  writers,  meant  the 
contradictory  of  your  opponent's  assertion,  and  thus  implies, 
what  indeed  was  a  feature  in  earlier  Logic,  the  existence  of 
an  opponent.  Dialectics  were  almost  always  in  the  form  of 
dialogue,  and  the  Socratic  mode  of  questions  and  answers 
was  adopted  as  the  acutest  method  of  argument.  , 

The  disputatious  spirit  of  the  Greeks  was  as  much  con- 
cerned about  the  victory  in  logomachy,  or  word-war,  as  about 
the  discovery  of  truth,  and  hence  arose  many  of  their  errors 
and  paradoxes.  This  spirit  of  controversy  and  the  constant 
keeping  in  sight  of  the  elenchus  has  pervaded  the  methods  of 
Logic  to  a  very  late  period. 

The  ignoratio  elenchi  is  the  ignorance  of  the  contradictory  of 
our  opponent's  assertion  which  we  display  when,  instead  of 
establishing  the  elenchus,  i.  e.,  proving  the  contradictory,  and 
thus  proving  his  conclu^on  or  assertion  false,  we  attempt  to 
establish  something  resembling  the  contradictory. 

As  it  is  not  our  purpose  to  reproduce  the  Grecian  techni- 
calities and  method,  let  us  get  rid  of  this  name  and  form,  and 
call  the  fallacy,  as  it  has  been  called  by  modern  writers,  the 
fallacy  of  irrelevant  concluMon. 

Those  who  employ  it — and  this,  it  may  be  remarked,  is  the 
most  common  and  practical  of  all  the  material  fallacies— 
generally  state  the  conclusion  as  a  fact,  and  when  asked  for 
the  premisses  or  proof,  are  compelled  to  present  such  as  dis- 
play the  irrelevancy  of  the  conclusion.  Thus,  one  asserts  the 
fact  that  "Alfred  the  Great  was  a  scholar,"  and  when  asked 
for  proof  says,  ^'Because  he  founded  the  University  of  Oxford.'* 
Now,  there  may  be  distinct  proofs  that  he  was  a  scholar,  but 
IS  K 


146  LOGIC. 

this   certainly  is  not  conclusive.      Let   us   state    the  syllo 

gism : 

Those  who  found  universities  are  patrons  of  learning; 

Alfred  the  Great  founded  the  University  of  Oxford ; 

Therefore  he  was  a  scholar. 

The  conclusion  is  irrelevant ;  the  true  conclusion  being,  frc  in 
these  premisses,  that 

He  was  a  patron  of  learning. 

If  polemical  writings,  and  especially  those  which  partake 
of  the  nature  of  popular  and  heated  controversy,  be  analyzed, 
this  will  be  found  to  be  the  standing  fallacy,  as  often  self- 
deceiving  as  deceiving  others,  and  responsible  for  much  of  the 
widespread  error  in  speculative  science. 

So  varied  is  its  nature  that  it  has  been  from  the  early  times 
known  under  various  names  and  presents  its  insidious  temp- 
tations to  all  kinds  of  persons. 

Perhaps  that  form  which  is  of  most  universal  application 
is  the  argumentum  ad  hominem,  the  unfair  appeal  to  personal 
opinions,  or  to  one's  vanity  or  prejudice.  After  exhausting  all 
the  arts  to  prove  a  thing  wrong  which  is  not  so,  the  argument 
closes  with  "  Well,  you  would  not  do  so !"  Even  in  matters 
of  religion  we  are  triumphed  over  by  the  adversary  by  a  refer- 
ence to  ourselves  and  our  own  imperfect  actions,  when  the 
question  concerns  the  abstract  truths  of  God's  holy  law.  This 
form  of  the  fallacy  needs,  then,  a  special  watch  as  the  most 
insidious. 

Next  in  enumeration  is  the  argumentum  ad  populum,  which 
is  the  former  fallacy  extended  from  one  individual  to  mar  y. 
from  personal  opinion  to  popular  prejudice. 

Unprincipled  demagogues  use  this  fallacy  continually  ;  and 
where  the  sophistry  would  be  apparent  to  any  single  mind 
gifted  with  common  sense,  the  enthusiasm  and  thoughtless 
spirit  of  a  mob,  moved  by  a  fiery  harangue,  is  blind  to  its 
unreasonableness.  This  may  be  called  the  logic  of  revolu* 
tions. 


\fATERIAT>,    OR    INFORMAL    FALLACIES.  147 

A  third  kind  of  in-elevant  conclusion  is  tlie  argmnentum  ad 
i^emmdiam,  or  appeal  to  the  modesty  or  sense  of  shame  of  our 
opponent,  hoping  that  he  will  not  presume  to  attack  respected 
authorlh'es  and  time-honored  ciistoms.  It  is  based  upon  the 
general  principle  that  natural  prejudice  is  in  favor  of  the 
existing  and  the  old.  Althougli  healthful  progress  may 
have  demonstrated  their  errors  and  provided  us  with  better 
methods,  the  cry  is  of  recreancy  to  our  fathers'  memories,  to 
old  associations,  to  History;  and  thus  the  world  has  been 
trammeled  and  clogged  by  what  professes  to  be  the  genius 
of  conservatism,  but  what  is  in  reality  the  genius  of  obstinate 
error. 

The  argumentum  ad  superstitionem  is  an  appeal  to  one's 
superstition,  from  which,  in  some  form  or  other,  few  men  are 
free;  ad  odium  is  to  one's  hatred;  ad  invidentiam,  to  envy; 
ad  amicitiam,  to  friendship.  Many  others  might  be  formed 
following  this  analogy.  Those  mentioned  are  sufficient  to 
illustrate  the  principle. 

Besides  these  forms  of  it-relevant  conclusion,  there  are  many 
which  have  been  proposed  in  pleasantry,  such  as  the  argu- 
mentum ad  baculinum,  and  others  which  Sterne  humorously 
refers  to  in  "  Tristram  Shandy." 

There  are,  however,  it  must  be  particularly  observed,  many 
cases  in  which  many  of  these  arguments  are  not  fallacies — in 
which,  indeed,  they  may  with  great  propriety  be  used,  clothed 
with  all  the  graces  of  rhetoric  and  imbued  with  all  the  spirit 
of  enthusiasm. 

The  argumentum  ad  hominem  is  not  a  fallacy  when  the 
design  is  to  teach  pure  truth,  and  when  no  unholy  passion  or 
emotion  of  man  is  appealed  to.  In  this  application  it  was 
used  by  our  Saviour  himself  to  the  Jews  on  many  occasions) 
with  great  force  and  beauty.  His  touching  and  yet  searching 
appeal  to  them  for  the  woman  taken  in  adultery  sent  them 
out  one  by  one  before  its  power.  Each  one  felt  the  argument 
and  admitted  the  conclusion. 


L48  LOGIC. 

His  arguments  in  favor  of  healing  on  the  Sabbath,  and  searek- 
Ing  the  Scriptures,  that  they  might  find  every  page  luminous 
with  Him  whom  they  denied,  were  examples  of  the  unfalla 
cious  and  powerful  use  of  this  form  of  reasoning. 

So,  too,  an  appeal  {ad  populum),  not  to  the  prejudices,  but 
to  the  conscientious  scruples  and  feelings,  of  a  multitude,  is 
without  fallacy,  and  is  productive  of  the  best  results. 

Many  customs,  long  honored  and  dear  to  every  heart — 
customs  national,  civic,  professional,  domestic — unmingled 
with  error,  unopposed  to  progress,  make  the  argumentum  ad 
verecundiam  a  most  proper  and  effective  appeal. 

But  such  is  the  waywardness  of  man  that  the  temptation  to 
fallacy  in  their  use  is  exceedingly  strong,  and  must  be  care- 
fully guarded. 

Argumentum  Ad  Rem  and  Ad  Judicium. 

Opposed  to  all  these,  when  used  as  fallacies,  are  two  forms 
of  valid  argument :  the  first  expresses  a  concentration  solely 
upon  the  reason  of  the  thing  itself,  and  is  therefore  called  the 
argumentum  ad  rem ;  the  second  is  when  the  appeal  is  made  to 
the  unbiased  exercise  of  the  individual  judgment ;  this  argu- 
ment is  called  argumentum  ad  judicium.  Many  writers  have 
increased  the  number  of  these  fallacious  argumenta  to  a  much 
greater  extent ;  but  those  given  are  the  principal  ones,  and 
will  sufficiently  indicate  the  process  by  which  they  are  coined 
when  needed. 

Changing  the  point  in  dispute. 

Another  form  of  the  "irrelevant  conclusion"  is  the  fallacy 
»f  changing  the  point  in  dispute,  in  which  one  of  the  parties 
in  a  long  and  diflBcult  controversy,  after  having  tried  in  vain 
to  establish  his  irrelevant  conclusion,  dextrously  shifts  his 
ground  from  the  point  in  dispute  to  some  other,  and  perti- 
naciously claims  that  to  be  true  which  has  not  been  disputed, 
while  the  true  matter  of  contention  is  left  without  an  honest 
confession  of  his  inability  to  prove  his  assertion.     For  ex- 


MATKfilAL,    OU    INFORMAL    FALLACIES.  141? 

ample,  a  person  uudertakes  to  prove  that  the  people  iu  general 
are  not  educated:  i.  e.,  he  first  denies  that  they  are;  but  failing 
of  this,  he  really  proves,  what  no  one  denies,  viz. :  that  all 
the  people  should  be  educated. 

Fallacy  of  Objections. 

It  has  been  remarked  that  Ignorance  may  state  in  a  few 
words  objections  against  Science  which  wise  men  could  not 
refute  in  whole  volumes.  The  truth  of  this  is  manifest.  The 
error  of  reasoning  from  the  statement  or  existence  of  these 
objections  to  the  falsity  of  the  science  is  one  of  the  forms  of 
irrelevant  conclusion  which  has  been  called  the  Fallacy  of 
Objections.  It  consists  in  asserting  that,  since  there  are  objec- 
tions against  a  Science,  that  Science  is  false ;  whereas  the  judg- 
ment demands  that  the  claims  of  the  Science  as  well  as  the 
objections  be  duly  stated,  and  that  the  turning  of  the  scale 
decide  whether  truth  or  error  predominate.  If  it  be  a  com- 
plicated system,  it  will  be  found  to  contain  portions  of  both ; 
if  an  abstract  theory,  it  will  stand  or  fall  by  such  a  test. 
This  fallacy  has  been  industriously  aimed  by  skeptics  against 
the  mysteries  of  the  Christian  faith,  but  it  soon  loses  its 
point  in  such  an  encounter. 

From  the  consideration  of  the  various  species  of  the  fallacy 
of  irrelevant  conclusion  which  have  been  mentioned,  and  the 
examples  given,  it  will  be  seen  that  it  is  in  all  its  forms  the 
standing  sophism  in  houses  of  legislative  convocation — that  it 
is  the  demon  of  debate.  Few  subjects  of  debate  are  so  ab- 
stract and  unit-like  but  that  dull  minds  will  find  room  to 
wander  about,  one  losing  the  very  point  in  question,  another 
concerned  about  a  crowd  of  details  which  have  little  or  no 
bearing  upon  it,  a  third  mistaking  the  fine  and  delicate  points 
of  the  logical  argument ;  some,  becoming  heated  in  the  con- 
troversy, will  lotte  their  temper  and  reasoning  })owers  together, 
and,  overpowered  by  the  truth  and  Logic  of  their  opponents, 
will  have  recourse  to  appeals  to  the  prejudices  and  interests 
13  » 


i  50  LOGIC. 

of  their  audience ;  and  others,  more  shrewd  than  just,  wiL 
seek  to  bring  by  similar  means  the  cause  and  persons  of  their 
adversaries  into  disrepute  by  the  light  arrows  of  ridicule  or 
the  more  ponderous  weapons  of  insult.  It  is  amidst  such 
scenes,  and  under  such  circumstances,  that  the  master  mind 
shows  itself  as  it  rises  over  the  storm  of  the  debate,  and  brings 
them  back  first  to  the  consideration  of  the  subject  in  dispute 
in  its  true  and  abstract  form.  Perhaps  the  most  striking 
illustration  of  this  is  found  in  our  own  Congressional  history. 
After  Mr.  Webster's  first  speech  on  '*  Foote's  resolution," 
many  senators  had  delivered  their  views,  and  much  sectional 
excitement  was  aroused.  Mr.  Webster  began  his  famous 
second  speech,  with  just  such  a  master-effort  to  come  back  to 
the  true  merits  of  the  controversy : 

"  Mr.  President,  when  the  mariner  has  been  tossed  for  many  days 
in  thick  weather  and  on  an  unknown  sea,  he  naturally  avails  himself 
of  the  first  pause  in  the  storm,  the  earliest  glance  of  the  sun,  to  take 
his  latitude,  and  ascertain  how  far  the  elements  have  driven  him  from 
his  true  course.  Let  us  imitate  this  prudence,  and  before  we  float 
farther  on  the  waves  of  this  debate,  refer  to  the  point  from  which  we 
departed,  that  we  may  at  least  be  able  to  conjecture  where  we  now  are. 
r  ask  for  the  reading  of  the  resolution  before  the  Senate." 

The  resolution  was  read ;  the  Senate  found  their  true  posi- 
tion, and  Mr.  Webster's  speech  is  as  masterly  for  its  logic  as 
for  its  oratory. 

(50.)  Verbal  Fallacies. 
There  is  still  a  most  important  class  of  invalid  arguments 
to  be  considered ;  it  is  that  growing  out  of  the  ambiguous .  or 
equivocal  meanings  of  words,  many  words  being  identically 
the  same,  and  yet  bearing  widely  different  meanings.  Thus, 
the  simple  word  line,  when  used  in  different  connections, 
means  many  distinct  things:  for  example,  a  cord  used  in  fislir 
ing ;  a  feiv  words  in  a  letter ;  an  arrangement  of  troops  or  ships 
in  battle  array ;  and  when  we  see  the  word  porter,  we  are  in 


VKllBAL    FALLACIES. 


151 


doubt  which  of  three  meanings  is  intended- -a  ijate  or  door 
keeper,  a  man  who  bears  burdens  or  a  kuid  of  malt  drink. 

In  most  such  cases,  however,  there  is  a  single  root  to  which 
we  may  trace  all  these  secondary  meanings;  thus  all  the 
meanings  of  a  line  refer  to  the  mathematical  definition  that 
it  is  length,  without  breadth  or  thickness,  and  all  the  uses  of 
porter  refer  to  the  Latin  word  which  signifies  to  bear. 

It  is  true  that  there  are  examples  of  words  spelt  alike  which 
have  different  etymologies,  but  these  are  few:  host  from 
hostis,  and  host  from  hostia  in  the  sacrifice  of  the  mass,  are 
examples  of  this;  so  dim  league  from  ligare,  to  bind,  and 
league  from  the  Latin  locus  or  distance  between  places,  con- 
tracted in  French  to  lieue,  as  the  word  focus  is  into  feu,  are 
examples  of  such  words.  With  these  few  illustrations  of  am- 
biguous terms,  let  us  see  how  they  are  used  in  argument. 

The  ambiguous  word  is   sometimes    the   middle  term  and 
sometimes  it  is  the  major  or  minor ;  in  most  cases,  however,  it 
assumes  the  former  place,  so  that  the  general  name  given  to 
this  form  of  verbal  fallacy  is  "  the  Ambiguous  middle." 
X  Y 


A  bank     is     the  border  of  a  stream. 
Z  X 


This   stone   building     is     a  bank. 
Therefore  This  stone  building  is  the  border  of  a  stream,  etc. 

Now,  if  this  glaring  and  absurd  fallacy  be  stated  by  sym 

bols,  we  shall  have — 

X  is  Y, 

Z  isX, 

Z  is  Y, 

which  is  the  form  of  a  valid  argument  in  the  first  figure     sc 
that  the  fault  lies  in  the  matter  of  the  propositions  ,vhich 
compose  the  argument,  and  not  in  the  form,  which  is  correct 
the  fallacy  then  must  be  classed,  with  such  an  investigation, 
fim  )ng  the  material  and  not  among  the  foiinal  fallacies.     But 


152  LOGIC. 

let  us  go  a  step  farther ;  since  "  a  bank"  in  the  major  premiss 
means  something  entirely  different  from  "a  bank"  in  the 
minoi;  they  are  in  reality  different  terms;  let  us  symbolize 
them  oy  different  letters,  and  calling  the  first  X,  let  us  call 
the  second  P ;  we  shall  have,  writing  by  symbols,  as  before, 

Xis  Y, 
Z  isP, 
Z  isY, 

a  formal  fallacy,  in  which  there  are,  contrary  to  the  rules  laid 
down.  Jour  terms  instead  of  three ;  and  this  comes  within  the 
province  of  Logic.  The  fallacy  of  Ambiguous  middle  has 
very  justly,  then,  been  called  by  logicians  a  semi-logical  fal- 
lacy ;  before  we  discern  the  ambiguity  it  is  a  inaterial  fallacy, 
with  which  Logic  is  not  concerned  ;  but  as  soon  as  we  discover 
the  ambiguity,  it  discloses  four  terms  which  make  it  a  formal 
or  logical  fallacy.  It  is  because  of  this  peculiarity,  and  be- 
cause it  is  so  very  much  used  in  common  life,  that  we  treat 
of  it  under  the  distinct  head  of  verbal  fallacies.  But  we  have 
said  that  it  is  not  only  in  the  middle  term  that  this  ambiguity 
occurs ;  it  also  happens  in  the  major  and  minor  terms,  and  is 
quite  as  sophistic  when  it  lurks  there  as  in  the  middle  term. 
We  have  therefore  discarded  the  title  "  Ambiguous  middle," 
as  applied  to  the  general  class,  preferring  "  Verbal  falla- 
cies," as  more  truly  illustrative  of  the  error  in  any  of  the 
terms. 

There  are  many  ways  in  which  words  come  to  be  used 
ambiguously,  and  we  shall  give  a  few  of  them,  with  illustra- 
tions ;  and  first  we  place  the  influence  of  Etymology. 

I.  Etymology. 

A  word  which  originally  meant  one  thing  now  means  quite 

another,  and  the  fallacy  consists  in  using  it  in  the  two  senses, 

m  two  propositions  of  the  syllogism.     Thus,  taking  the  first 

meaning  of  pagan  to  be  a  villager  (pagan us*),  and  its  present 

*  From  pagus,  a  villa:;e. 


VKIilJAL    BWLLACIES.  153 

aieaning  to  be  a  believer  in  some  other  religion  than  that  of 
Christ,  we  have — 

A  par/an  is  a  disbeliever  in  Christ ; 

Every  villager  is  a.  pagan; 

Every  villager  is  a  disbeliever  in  Christ. 

Akin  to  this,  and  indeed  ranging  under  the  general  rubjeoi 
of  etymology^  is  the  use  of  paronyms,  or  paronymous  ivords. 

Paronymous  words  are  the  noun  substantive,  adjective, 
verb,  etc.,  belonging  to  each  other  and  springing  from  the 
same  root.  To  project,  project,  projection,  projector,  etc.  are 
paronyms,  springing  from  the  Latin  compound  of  pi'o  and 
jaceo.  So  presume  (in  its  two  senses), presumption,  presumptive, 
presumptuous,  etc.  are  paronyms  growing  from  the  root  presume. 

Take  the  following  example,  in  which  the  ambiguity  will 
lie  in  the  middle  term  : 

Presumption  is  impertinence ; 

That  the  sun  shines,  I  presume  (or,  is  my  presumption) ; 

Therefore  I  am  impertinent  (in  asserting  that  the  sun  shines). 

It  will  be  remembered  that  the  true  logical  form  of  the 
minor  premiss,  which  is  usually  written,  "  I  presume  that  the 
Bun  shines,"  is — 

subj.  pred. 


That  the  sun  shines     is     presumed  by  me. 
Again : 

To  propose  a  railroad  is  a  project  (or  a  projector's  work). 
This  man  proposed  a  railroad. 
Therefore  He  is  a  projector  (or  visionary  man). 

In  which  the  ambiguity  lies  in  the  major  term.  Now,  no 
one  can  work  advisedly  without  making  projects,  whereas 
one  of  the  meanings  of  projector  is  a  scheming  and  visionary 
man  who  ought  not  to  be  relied  upon. 

II.  Fallacy  of  Interrogations. 

This  is  a  use  of  two  or  more  terms  in  a  question,  making 
thus  in  reality  two  questions,  requiring  two  distinct  answers, 


154  LOGIC. 

and  the  ambiguity  lies  in  the  single  answer  given  to  both 
It  is  common  for  those  who  use  this  fallacy  to  express  but 
one  question,  while  the  other  is  implied.  Thus,  if  a  man 
who  has  always  been  temperate  is  asked,  "  When  he  gave  up 
drinking  f^  the  implied  question  is,  "  Did  he  ever  drink  f^  and 
then,  if  so,  when  did  he  cease  ?  or,  in  the  celebrated  inquiry 
of  King  Charles  II.,  "Why  a  live  fish  does  not  add  to  the 
weight  of  a  vessel  of  water  f  the  implied  question  being  "  Does 
a  live  fish  addf  etc.,  and  if  so,  "why?"  etc.,  or  a  witness 
may  be  asked.  Where  were  you  when  the  prisoner  murdered 
the  deceased  ?  which  would  imply  what  remains  to  be  proved, 
viz.,  that  he  did  murder  him.  This  fallacy,  which  is  called 
by  the  writers  Fallacia  plurium  interrogationum,  is  made 
more  subtle  by  the  number  and  closeness  of  resemblance 
of  the  points  included  in  the  questions. 

III.  Amphibolous  Sentences. 

Sometimes  the  ambiguity,  instead  of  residing  in  the  words 
which  compose  the  argument,  lies  in  the  construction,  and 
thus,  by  different  punctuations,  we  have  double  and  opposite 
meanings.  This  passes  from  the  ambiguous  words  to  amphibo- 
lous sentences.  Among  the  most  celebrated  of  these  is  the 
response  of  the  Delphic  oracle  to  Pyrrhus  when  he  went  to 
encounter  the  Komans : 

Aio  te  jEacida  Romanos  viiicere  posse, 
Ibis  redibis  nunquam  in  bello  peribis. 

In  the  first  line,  either  accusative  may  be  taken  with  the 
infinitive,  thus  making  either  "  Pyrrhus "  or  "  the  Eomans " 
able  to  conquer;  and  in  the  second,  nunquam  may  qualify 
either  redibis  or  peribis. 

So  also  in  the  Nicene  Creed,  we  have,  in  reference  to  our 
Saviour,  the  words,  "  being  of  one  substance  with  the  Father, 
by  whom  all  things  were  made." 

The  latter  clause,  so  manifestly  introduced  by  the  Council 


VERBAL    FALLACIES.  165 

to  declare  the  creative  power  and  Godhead  of  Christ,  in  reality 
by  strict  rhetoric  applies  to  "  the  Father.'' 

The  name  given  to  this  fallacy  is  the  fallacy  of  amphib- 
olous'^ sentences,  i.  e.,  tossed  from  one  to  another  with  a  doubt- 
ful meaning. 

Causes  of  Ambiguity. 

Having  mentioned  the  various  kinds  of  ambiguity  in  words, 
we  come  to  consider  why  words  have  two  or  more  meanings. 

We  have  already  seen  that  many  words  expressing  simple 
primitive  ideas  grow  by  usage  to  have  other  meanings,  in 
which,  however,  the  primitive  idea  is  to  some  extent  retained ; 
thus,  line,  in  all  its  meanings,  adheres  to  the  mathematical 
notion  of  extension  in  length. 

Now,  without  being  able  to  trace  the  exact  process  in  all 
cases  by  which  a  word  is  thus  gradually  changed,  we  find 
that  it  ranges  itself  under  one  of  these  heads  :  1.  Resemblance; 
2.  Analogy;  3.  Association;  4.  Ellipsis;  5.  Accident. 

1.  Resemblance.  Many  things  bear  the  same  name  from 
their  actual  similarity  in  appearance.  Thus,  in  carpentry,  a 
dove-tailed  joint  is  so  called  from  its  similarity  to  a  dove's  tail, 
or  a  spear  of  grass  from  its  resemblance  to  the  military  weapon, 
a  spear.  So  in  the  military  art  a  "  priest-cap  "  or  "  swallow- 
tail "  is  a  redoubt  so  named  from  its  actual  resemblance  to 
one  of  these  two  things,  and  a  ''crow's  foot"  takes  its  name 
from  the  form  of  a  bird's  talons. 

2.  Analogy.  Our  ordinary  speech  is  full  of  the  use  of  this 
figure  of  speech,  and  this  fact  has  contributed  to  the  am- 
biguity in  many  words.  As  resemblance  is  a  similarity  iu 
appearance,  analogy  is  a  similarity  in  use,  purpose  or  relation. 
Thus,  we  speak  of  the  arm  of  a  chair,  because  it  holds  the 
relation  to  the  chair  which  the  arm  does  to  the  human  body ; 
and  thus  an  arm-chair  is  a  chair  which  has  arms. 

We  speak  equally  of  a  sweet  food,  or  a  siveet  sound,  because 

♦  a/i(pi  and  ISaXXu. 


156  LOGIC. 

there  is  a  similarity  between  the  relations  of  the  food  to  the 
palate  and  the  sound  to  the  ear.  So  a  sour  lemon  and  a  sour 
individual  create  relatively  similar  effects  upon  the  taste  and 
upon  the  mind. 

Ambiguity  of  resemblance  and  of  analogy  are  both  pr> 
duced  and  perpetuated  by  the  use  of  metaphor  and  compari- 
son, in  our  ordinary  discourse,  and  a  wayward  fancy,  express- 
ing itself  in  the  social  exaggerations  of  the  day,  is  robbing 
some  of  our  best  words  of  their  true  shades  of  meaning ;  for 
example,  siveet,  lovely,  horrid,  agony,  wretch,  are  deflected  from 
their  original  meanings  entirely. 

An  argument  from  analogy  may  lead  to  probability,  but  is 
fallacious  when  it  claims  a  certain  condition,  but  it  may  well 
be  used  to  corroborate  and  strengthen  other  arguments  as  an 
additional  likelihood. 

3.  Association.  By  this  we  mean  the  connection  of  parts 
in  the  same  structure  or  institution,  or  to  produce  a  single 
result.  Thus,  a  door  is  the  opening  in  the  wall  or  the  swing- 
ing shutter  that  closes  it.  Faith  is  belief,  and  "the  Faith"  is 
the  system  of  Christianity.  Shot  is  the  leaden  pellet :  a  good 
shot  is  either  the  person  who  shoots  or  the  effect  of  the  shot. 

It  is  by  the  association  of  ideas,  which,  unlike  our  examples, 
are  subtle  and  difficult  to  fix  and  determine,  that  fallacies 
have  grown  out  of  this  ambiguity ;  and  such  is  the  want  of 
correctness  in  the  language  of  the  great  number  of  people 
that  the  tendency  to  this  fallacy  of  words,  expressing  asso- 
ciated ideas,  is  particularly  strong  and  dangerous. 

4.  Ellipsis.  Another  habit  into  which  men  naturally  fall, 
in  trying  to  avoid  the  use  of  many  words,  and  words  convey- 
ing thoughts  which  the  mind  will  readily  supply  without  theii 
being  expressed,  is  the  use  of  elliptical  language.  While  iu 
most  cases  this  is  harmless  and  even  profitable,  in  some  it 
leads  to  error.  Thus,  we  speak  constantly  of  Scott,  Byron, 
etc.,  when  we  mean  their  works  or  their  persons.  We  use  the 
form  "to  my  father's,"  "at  Mrs.  Smith's,"  when  we  mean  the 


VERBAL    FALL/VCIES.  157 

houses  or  "parties"  of*  these  persons,  and  such  ellipsis  is 
always  understood ;  but  many  persons  are  deceived  in  their 
business  relations  by  such  ellipsis  as  the  statemeni  of  another''^ 
wealth  at  so  many  thousands  of  dollars,  when  in  reality, 
although  it  may  produce  the  interest  on  such  a  sum,  it  can- 
not be  made  available  for  anything  like  the  amount  of  tlu 
principal  sum  mentioned. 

5.  Accident.  It  seems  in  certain  cases  as  though  a  wonl 
had  assumed  two  meanings  in  a  manner  inexplicable  and 
accidental.  Such,  for  example,  is  the  word  light,  which  is 
equally  opposed  to  heavy  and  dark,  and  which  in  conduct 
means  the  opposite  of  serious  or  dignified.  But  even  in  such 
a  case  we  shall  find  one  idea,  however  subtle,  pervading  them 
all,  and  that  is  the  removal  of  a  covering  of  some  sort ;  thus, 
light  removes  the  pall  or  covering  of  darkness  ;  the  incumbent 
weight  of  something  heavy ;  the  just  restraints  of  dignity  and 
sobriety.  In  strict  truth,  then,  there  is  no  accidental  am- 
biguity, for,  although  there  may  be  words  in  the  double  mean- 
ings of  which  we  can  discover  no  relation  to  a  single  idea, 
that  relation  undoubtedly  exists,  and  by  a  profound  research 
the  number  of  such  words  would  be  very  much  diminished. 

Many  words  are  forced  into  a  double  meaning  by  a  populai 
or  political  use,  which  may  be  called  accidental,  but  which  in 
reality  is  designed  by  one  party  as  au  equivoque,  or  strata- 
gem, in  the  way  of  retort  upon  the  other.  It  was  thus  with 
the  use  made  of  the  word  Pretender  by  the  English  Jaco 
bites.  When  it  became  treasonable  in  any  way  to  maintair 
the  claims  of  James  Stuart,  the  son  of  James  II.,  who  wa/ 
called  "the  Pretender,"  they  toasted  him  in  the  well-knowi 

verses : 

God  bless  the  King;  God  bless  the  Faith's  Defender; 
God  bless — no  harm  in  blessing — the  Pretender. 
But  which  is  the  Pretender?  which  the  king? 
God  bleas  us  all — that's  quite  a  different  thing. 

It  is  evident  that  such  a  use  of  the  word  would  deceive  m 
one;  nor  was  it  indeed  so  desiirned,  but  rather  to  violate  the 

14 


1 58  LOGIC. 

spirit  and  yet  adhere  to  the  letter  of  the  law.     The  true 
argument  used  by  the  adherents  of  the  new  dynasty  was-  — 

Those  who  aid  a  pretender  to  the  English  throne  deserve  punish- 
ment. 
James  Stuart  is  a  pretender. 
Those  who  aid  James  Stuart  deserve  punishment. 

It  must  be  understood  that  pretender  in  both  premissea 
has  the  same  meaning — i.  e.,  false  claimant. 

But  there  is  still  another  form  of  ambiguity  which  leads 
to  fallacious  arguments ;  it  is  where  the  ambiguity  lies  not  in 
words,  but  in  the  context ;  or  where  our  assertion  means  one 
thing  when  taken  in  a  general  sense,  and  quite  another  if 
considered  in  a  special  sense.  Of  these  fallacies,  arising  from 
ambiguity  in  the  context,  there  are  two  kinds : 

1.  The  fallacy  of  accidents. 

2.  The  fallacy  of  division  and  com/position. 

Under  the  first  head  are  included  the  Fallacia  accidentis, 
and  the  Fallacia  a  dicto  secundum  quid  ad  dictum  simplidter 
These  are  the  converse  of  each  other. 

Fallacia  accidentis. 
This  is  where,  in  one  premiss,  we  assert  something  of  a 
subject  in  a  general  sense,  and,  in  the  other,  place  upon  that 
subject   some   accidental  peculiarity  which  will    lead    us   to 
error  in  the  conclusion,  thus  : 

Things  bought  in  market  we  eat. 
Raw  meat  is  a  thing  bought  in  market. 
Therefore  Eaw  meat  is  what  we  eat. 

Here  the  middle  term  is  things  bought  in  market,  and  it  is 
considered  in  the  major  premiss  as  to  its  essence,  viz. :  that 
these  things  are  in  market  for  general  use  as  food;  in  tne 
minor  we  lose  sight  of  its  essence,  and  only  regard  some  acd- 
dent  of  it,  viz. :  that  the  meat  bought  in  market  is  raw.  Thus, 
in  reality,  the  error  is  thrown  upon  the  middle  term,  which 
is  shown  to  be  not  one,  but  two  distinct  terms,  and  the  fallacy 
is  thus  exposed. 


VERBAL    FALLACIES.  159 

The  other  t'oriii  of  this,  which  for  shortness  is  called  the 
Fallacy  of  Quid,  may  be  translated  reasoning  from  the  re- 
strided  or  limited  sense  of  a  term  (secundum  quid — /.  e.,  ali 
quid  in  the  monkisli  I^atin),  to  its  broad  or  unrestricted  u.^e  (ucf 
dictum  simpliciter).     Thus : 

This  man  is  innocent  (of  a  certain  crime)  ; 
But  the  innocent  (entirely)  are  sure  of  Heaven  ; 
.     Therefore  This  man  is  sure  of  Heaven. 

Fallacy  of  Division  and  Composition. 
In  this  faUacy  the  middle  term  is  used  in  its  collective  or 
additive  sense  in  one  premiss,  and  in  its  distributive  sense  in 
the  other.  When  the  middle  term  is  used  collectively  in  the 
major  premiss,  and  distributively  in  the  minor,  the  fallacy  is 
of  "  Division  ;"  when  the  reverse  takes  place,  it  is  a  fallacy  of 
"  Composition."     The  following  are  examples  : 

Fallacy  of  Division. 
The  Christians  (as  a  sect)  were  persecuted  at  Rome. 
Constantine  was  a  Christian  (individually). 
Therefore  He  was  persecuted  at  Rome. 

Fallacy  of  Composition. 
Three  and  two  are  two  numbers  (distributively). 
Five  is  three  and  two  (additively). 
Five  is  two  numbers. 

Positive  and  Negative  Intention. 

Akin  to  these  fallacies  are  those  absurd  conclusions  reached 

by  a  play  upon  certain  negative  words,  such  as  nothing  and 

no  when  used  as  an  adjective ;  thus, 

Nothing  is  better  than  Heaven. 
A  shilling  is  better  than  nothing. 
Therefore    A  shilling  is  better  than  Heaven. 

No  cat  has  two  tails. 

Every  cat  has  one  tail  more  than  no  cat. 

Every  cat  has  three  tails. 

In  these  examples  the  middle  terms  nothing  and  no  cut  are 
taken  in  a.  positive  sense  in  the  major  premiss,  as  though  they 


160  LOGIC. 

expressed  living  or  existing  things,  while  iu  reality  they  inean 
non-existence.  In  the  minor  premiss  they  are  taken  in  theii 
true  negative  sense. 

The  best  method  of  refuting  them  is  to  deny  the  major 
premiss,  or  to  demand  that  it  be  put  in  other  words,  thus . 

It  is  not  true  of  anything  that  it  is  better  than  Heaven  ; 
which  will  foil  the  one  who  wishes  to  draw  the  absurd  con- 
clusion.     It  should   be  observed   that  such   arguments  are 
really  used  only  in  sport,  but  it  is  well  to  detect  and  under- 
stand the  error  which  they  contain. 

(61.)  The  Manner  of  Removing-  Ambiguity  in  Terma. 

The  true  method  of  ridding  ourselves  of  this  ambiguity  of 
terms  in  argument  is  to  demand  a  definition  in  each  case,  and 
to  keep  our  terms  distinct  when  thus  defined.  It  will  not,  in 
most  cases,  be  necessary  to  give  a  real  definition,  as  a  nominal 
one  will  answer  every  purpose.  The  ambiguity  is  usually  such 
that  by  giving  the  true,  limited  and  exact  name  (which  is  the 
province  of  a  nominal  definition)  we  shall  detect  and  remove  it. 

In  many  cases  where  the  fallacies  consist  of  a  number  of 
arguments  and  many  ambiguous  terms,  the  first  thing  to  be 
done  is  to  disentangle  the  web  of  sophistry  by  writing  them 
out  in  full  and  in  due  order,  and  then,  after  detecting  the 
terms  in  which  the  ambiguity  lies,  to  demand  a  definition  in 
a  few  but  plain  and  conclusive  words  in  every  case. 

The  equivocal  nature  of  the  word  becomes  apparent  if  wf 
change  the  language,  as  in  the  translation  of  the  familiai 
example  into  Latin — 

Light  is  contrary  to  darkness, 
Feathers  are  light. 
Therefore  Feathers  are  contrary  to  darkness, 

we  shall  have — 

Lux  est  contraria  tenebris. 

Plumse  sunt  leves. 

Plumae  sunt  contrariae  tenebris.* 

*  Latham's  Logic,  p.  221. 


THP:    fallacy    of    PUOliAlilLlTIES.  16 1 

This  change  of  lauguage,  it  will  be  seen,  is  of  the  nature  of 
a  detinition. 

(52.)  The  Fallacy  of  Probabilities,  or  the  Calculation 

of  Chances. 

This  consists  in  stating  two  probable  premisses,  and  then 
drawing  a  certain  or  more  probable  conclusion,  as  though  the 
number  of  probabilities  coniljined  amount  to  certainty,  where- 
as, in  most  cases,  the  conclusion  will  be  less  probable  than 
either,  thus : 

Those  who  have  the  plague  prohahly  die; 
This  man  probably  has  the  plague  ; 
Therefore  He  will  (certainly)  die. 

Whereas,  suppose  ten  out  of  twelve  of  those  who  have  the 
plague  die,  then  if  we  express  certaintij  by  the  number  1,  that 
probability  is  expressed  by  the  fraction  yI  or  f ;  and  if  it  is 
an  even  chance  whether  or  not  he  has  the  plague,  that  proba- 
bility will  be  expressed  by  \.  The  probability  of  the  conclu- 
sion, therefore,  will  be  f  X  i  =  A'  ^r  as  ^  is  the  expression 
for  perfect  doubt,  i.  e.,  an  even  chance  of  his  living  or  dying, 
he  is  less  likely  to  die  than  to  live,  his  chances  of  dying  being 
5  out  of  12,  and  of  living,  7  out  of  12. 

This  fallacy  is  practically  used  in  times  of  sickness  and 
mortality,  when  fears  of  evil,  excited  by  nervousness,  affection, 
etc.,  place  an  anticipated  conclusion  for  the  true  one. 

When,  instead  of  one  syllogism  or  enthymeme,  many  are 
combined  to  make  a  compound  argument,  and  the  errors  of 
probability  are  thus  multiplied,  the  result  will  be  at  once 
farther  from  the  truth  and  more  difficult  to  detect. 

Let  us  deduce  then  a  simple  rule  for  the  calculation  of 
probabilities.  The  subject  has  been  called  "the  doctrine  of 
chances." 

When  we  speak  of  chance,  we  really  mean  probable  results 
of  God's  laws,  and  in  the  use  of  either  word  we  express  our 
ignorance  of  the  connection  between  natural  causes  and  effect*' 
14  *  L 


162  LOGIC. 

Now,  as  that  iguorance  may  be  partial  or  entire,  we  are  thrown 
upon  a  calculation  of  the  chances,  and  we  shall  find  that  the 
probability  ranges  between  the  two  extremes,  certainty  and 
impossibility.  We  do  not  pretend  to  assert  by  this  that  man 
may  divine  the  results  of  God's  doings  in  the  future ;  but  that 
according  to  the  action  of  natural  laws  and  the  sequence  of 
an  established  order,  we  may  approximate  to  the  truth  with- 
out assuring  ourselves  of  it. 

Thus,  in  throwing  dice,  we  cannot  be  sure  that  any  single 
face  or  combination  of  faces  will  appear ;  but  if,  in  very  many 
throws,  some  particular  face  has  not  appeared,  the  chances  of 
its  coming  up  are  stronger  and  stronger,  until  they  approach 
very  near  to  certainty.  It  must  come ;  and  as  each  throw  is 
made  and  it  fails  to  arjpear,  the  certainty  of  its  coming  draws 
nearer  and  nearer. 

The  probability  of  a  single  event  depends  upon  the  number 
of  chances  of  which  it  is  one.  Thus,  if  A  is  in  a  single  action 
where  10  men  are  killed,  his  company  numbering  50,  the 
chance  which  each  man  stands  of  being  killed,  and  conse- 
quently that  of  A,  is  -^  or  \.  If  we  subtract  \  from  1,  or 
certainty,  we  shall  have  -f  for  his  chance  of  being  saved.  The 
calculation  of  probabilities  becomes  more  complicated  where 
the  events  are  combined.  Thus,  if  in  a  second  action  10  men 
more  are  killed,  his  chance  of  being  killed  in  this  last  action 
is  as  10  to  40,  or  J,  and  that  of  his  being  saved  |.  If  now  we 
would  determine  his  chance  of  being  saved,  after  both  actions, 
we  must  multiply  the  two  chances 'together :  |-  X  f  =  i^  =^ 
I,  which  is  as  it  should  be,  since  20  men  are  lost  of  the  orig- 
inal 50  and  30  remain  ;  his  chance  of  being  among  the  latter 
should  be  as  30  to  50,  or  f . 

It  is  upon  this  principle  of  calculating  chances  that  insur- 
ance companies  are  founded,  and  it  finds  a  benevolent  issue 
and  scope  particularly  in  those  life-assurance  companies  which, 
demanding  but  a  small  percentage,  making  a  large  aggregate, 
are  thus  enabled  to  pay  to  widows  and  orphans  an  honorable 


POPULAR    FA1.LA(MHS.  163 

support,  snatching  out  ol'  llic  jaw.s  of  deiitli  tlie  means  of  life 
and  social  comfort. 

It  is,  however,  upon  a  false  study,  or  rather  in  an  ignorant 
and  fatal  reliance  upon  this  principle,  that  those  wlio  frequent 
gaming-houses  throw  away  their  means,  reputation  and  life ; 
for  the  true  gainers  are  not  the  frequenters  of  the  gaming- 
table, but  the  keepers,  who  are  acting  upon  this  very  doctrine 
of  chances.  By  a  calculation  of  chances  it  is  found  that,  in 
the  long  run,  the  keeper  of  a  gaming-house  must  win  in  almost 
every  kind  of  game  played,  while  only  an  occasional  player, 
with  what  is  called  a  marvelous  run  of  luck,  chances  to  win 
largely. 

The  subject  of  probabilities,  which  in  its  right  use  is  not 
fallacious,  but  is  reduced  to  arithmetical  accuracy,  has  been 
placed  under  the  general  head  of  Fallacies,  because  of  its 
being  so  liable  to  fallacious  use,  and  so  much  employed  thus. 
Mingling  as  it  does  with  the  superstition  in  our  nature,  we 
deem  those  things  more  probable  than  they  are  which  we 
desire  or  fear. 

The  wish  is  father  to  the  thought  for  pleasant  hopes,  and 
presentiments  of  evil  are  taken  for  its  probable  coming  in  our 
gloomy  periods.  We  give  a  rule  by  the  use  of  which  all  this 
may  be  avoided. 

Rule. — The  probability  of  any  event  is  expressed  by  a  frac- 
tion of  which  the  numerator  is  the  number  of  chances  in  its 
favor,  and  the  denominator  is  the  sum  of  all  the  chances ; 
and  the  probability  of  any  two  or  more  events  jointly  occur- 
ring will  be  obtained  by  multiplying  together  the  fractions 
expressing  the  probability  of  each. 

(53.)  Popular  Fallacies. 

It  will  be  well,  before  closing  the  chapter  on  Fallacies,  to 

show  their  practical  use,  especially  in  a  popular  illustration 

A  community,  a  state,  a  nation,  will   unite  upon  a  fallacy 

from  which  it  will  be  a  sort  of  social  treason  to  dissent :  ar< 


164  LOGIC. 

age  will  be  tinctured  by  error,  pervadiug  all  classes,  which 
only  the  innovation  of  a  succeeding  age  can  remove ;  a  false 
principle  will  cling  to  human  nature,  in  the  mass,  during 
many  centuries,  which  the  philosophic  mhid  can  only  deplore 
in  secret. 

It  will  be  our  purpose,  then,  to  put  forth  some  of  the  sim- 
plest forms  of  popular  fallacy,  beginning  with  the  most  gene- 
ral.  Some  of  these  have  been  already  mentioned  in  their  logi- 
cal places,  as  the  different  forms  of  irrelevant  conclusion,  etc. 

1.  The  fallacy  which  is  expressed  by  the  adage.  Nil  de 
mortuis  nisi  honum.  There  is  a  just  meaning  to  this  indeed; 
it  is  that  the  tongue  of  private  enmity  should  be  silenced — 
that  we  should  consider  Death  as  having  adjusted  all  difficul- 
ties as  between  man  and  man,  and  awed  our  mortal  infirmi- 
ties into  a  silence  and  forgetfulness  of  the  evil  which  existed 
in  him  who  is  now  dead.  So  far  the  adage  is  good ;  but  when 
it  becomes  a  principle  in  public  morals,  when  it  tinctures  the 
historian  and  the  historical  biographer,  who  should  deal  with 
the  dead  as  with  living  defendants,  arraigned  for  trial,  its  evil 
nature  is  apparent.  When  it  eulogizes  the  dead  at  the  ex- 
pense of  the  living,  and  runs  riot  in  obsequious  praises  and 
flattering  epitaphs,  it  assumes  its  most  sophistic  form.  "The 
same  man,"  says  Jeremy  Bentham,  "who  bepraises  you  when 
dead  would  have  plagued  you  without  mercy  when  living." 
The  reason  of  this  is  apparent.  A  dead  man  cannot  be  a 
rival ;  he  incurs  nobody's  envy,  and  is  removed  from  all  the 
results  of  malice. 

II  Not  unlike  the  preceding  is  the  fallacy  conveyed  in  the 
trite  saying,  De  gustibus  non  est  disputandum.  This  is  used 
fallaciously  to  put  a  stop  to  controversy  ;  the  assertion  imply- 
ing that  as  God  gave  man  each  his  own  taste,  one  taste  is  as 
good  as  another.  But  all  our  systems  of  education  teach  us 
that  this  is  not  true— that  there  is,  on  every  subject  which 
comes  under  the  dictum  of  taste,  a  true  standard  which  can 
and  ought  to  be  used.     It  certainly  is  better  to  put  an  end  tr 


POPULAR    FALLACIES.  165 

controversy  ly  saying  that  it  is  better  to  differ  than  to  became 
excited  and  quarrel,  than  falsely  to  state  that  there  can  be  no 
dispute  about  tastes. 

III.  There  is  a  fallacy  which  particularly  assails  patriotism : 
it  is  the  fallacy  of  asserting  that  any  one  form  or  system  of 
government  is  abstractly  the  best.  The  Russian  deems  that 
men  cannot  be  controlled  in  masses  without  single  autocratic 
power ;  the  Englishman  defies  the  world  to  pick  a  flaw  in  hit; 
limited  monarchy  and  superb  aristocracy ;  while  the  Ameri- 
can boldly  declares  that  the  best  government  is  the  democratic 
representative  form.  Where  such  men  as  Milton  and  Locke 
have  "  astonished  the  world  by  signal  absurdities  "  in  their 
models  of  government,  we  might  be  sure  that  its  theory  must 
be  diflacult;  but  the  truth  is,  there  is  no  abstract  theory  of 
human  government. 

Asiatic  barbarians,  when  they  leave  their  patriarchal 
wandering  life,  as  in  Russia,  and  come  into  the  first  corrup- 
tions of  a  half-civilized  life,  must  be  governed  by  despotic  power : 
they  cannot  be  republican  ;  while  on  the  other  hand,  it  is  only 
where  education  is  general  among  the  people — that  they  may 
know  their  wants,  and  how  to  supply  them,  and  where  indi- 
vidual honesty  and  virtue  are  everywhere  felt,  that  no  undue 
means  may  be  taken  to  bring  about  such  an  end — that  a 
democratic  government  is  the  right  one.  Then,  in  this  freest 
form  there  is  a  reciprocal  influence  between  the  government 
and  that  upon  which  it  is  founded.  A  free  government  en- 
lightens and  purifies  the  people,  while  the  enlightenment  and 
purity  of  the  people  strengthen  and  ensure  the  government 
under  which  they  live. 

IV.  There  is  a  popular  fallacy  which  may  be  called  Sweep- 
ing classifications.  It  consists  in  ascribing  to  an  individual 
something  really  belonging  to  another  individual,  only  because 
the  two  happen  to  be  of  the  same  class ;  thus,  during  the 
French  Revolution,  when  the  fate  of  Louis  XVI.  seemed  to 
hang  upon  a  thread,  one  pamphlet  was  issued  with  the  title 


166  LOGIC. 

'  The  Crimes  of  Kings."  Now,  as  there  had  been  many  bad 
kings  in  Europe  and  not  a  few  in  France,  Louis  XV'I.,  the 
best  of  them,  was  put  into  the  category  of  condemnation 
simply  because  he  was  a  king. 

Thus  misusing  the  adage  "  ab  uno  disce  omnes,^'  govern- 
ments and  institutions,  both  secular  and  religious,  are  blamed 
because  some  of  their  members  indulge  in  crimes  entirely 
their  own.  The  entire  body  is  made  to  share  in  the  condem- 
nation because  the  few  are  guilty. 

V.  Space  would  fail  in  which  to  enumerate  the  current 
and  manifest  popular  fallacies,  most  of  which  are  used  in 
legislatures  and  councils,  and  are  considered  in  the  light  of 
shrewd  and  dextrous  diplomacy.  There  is  the  "  no  precedent 
argument."  It  is  stated  thus :  "  The  plan  proposed  is  entirely 
new.  This  is  certainly  the  first  time  such  an  idea  has  been 
broached  in  this  honorable  house ;  and  therefore  the  secret 
hope  is  that  this  house  will  not  now  entertain  it." 

Next,  we  have  personalities  introduced,  laudatory  or  abu- 
sive, by  which  to  turn  the  current  of  the  argument. 

Another  form  is  the  assertion  with  regard  to  any  measure 
that  as  "  no  complaint  has  ever  been  brought  against  it  be- 
fore, it  must  be  a  good  one." 

But  perhaps  the  most  insinuating  form  of  popular  fallacy 
is  that  of  authority  by  which  a  man  is  required  to  join  one  oi 
the  other  party  in  every  question,  thus  causing  the  young 
ignorantly  and  prematurely  to  commit  themselves  to  views 
and  measures  which  later  experience  teaches  them  to  be 
wrong ;  if  then  they  change  they  are  traitors  or  turncoats,  if 
it  bt  a  national  or  political  question,  and  fickle  and  unreli 
able,  if  it  be  of  a  less  general  nature.  It  is  lamentable  to 
see  party  guides  bringing  those  under  their  control  forward 
to  swell  the  ranks  of  their  party,  and  those  thus  introduced 
glorying  in  their  new  distinction,  when  self-interest  and  no^ 
truth  has  been  the  motive  on  both  sides. 


CHAPTER    XI. 

THE  FUNDAMENTAL   LAWS   OF  THOUGHT,  OR   FIRS! 
PRINCIPLES    OF  REASON. 

Having  thus  explained  the  various  logical  processes  hy 
which  the  mind  seeks  to  establish  truth  and  detect  error,  and 
having  explained  the  subject  of  fallacies  in  form  and  in  mat- 
ter, the  existence  and  prevalence  of  which  show  the  necessity 
of  an  exact  system  of  logic,  it  will  now  be  proper  to  lay 
down  for  students  the  fundamental  laws  of  thought,  or  what 
may  be  called  the  first  principles  of  reason. 

A  primary  principle  is  one  which  has  no  cause  or  reason 
behind  it  upon  which  it  depends.  It  is  recognized  as  true 
without  proof,  for  it  cannot  be  proved ;  it  is  necessary,  uni- 
versal and  underivable — that  is,  it  belongs  to  mind  as  a  neces- 
sary part  of  its  existence,  it  belongs  to  all  minds,  it  depends 
on  nothing  antecedent  of  itself. 

The  number  of  these  first  principles  has  been  more  or  less 
extended  by  difierent  schools  of  philosophy,  but  there  are 
four  upon  which  most  philosophers  are  agreed,  viz. :  Iden- 
tity,   CONTRADICTION,    EXCLUDED    MIDDLE    and  the  laW    of 

REASON  AND  CONSEQUENT.     Upou  thcsc  as  a  basis  the  sys- 
tem of  Logic  is  reared  as  a  superstructure. 

I.  Identity.  With  the  belief  or  cognition  of  our  r>wn 
existence  comes  the  belief  that  whatever  is,  is,  or,  in  the  lan- 
guage of  the  older  schoolmen,  Omne  ens  est  ens.  In  regard 
to  any  object  the  mind  at  once  affirms  it  of  itself,  and  can- 
not think  of  it  but  as  existing.  The  law  of  identity,  it  will 
be  readily  observed,  is  the  principle  upon  which  logical 
affirmative  propositions  and  definitions  are  formed.     Thus,  in 

It': 


1(J8  LOGIC. 

the  proposition  All  A  is  B,  the  identity  of  the  whole  of  A 
with  a  part  of  B  is  set  forth. 

II.  Contradiction.  Simultaneously  with  this  intuitive 
belief  in  identity  appears  the  second  principle,  Contradiciion. 
or,  in  the  words  of  Sir  William  Hamilton,  more  properly 
non-contradiction,  which  has  been  called  the  highest  of  all 
logical  laws,  which  gives  sole  value  to  identity.  The  law  of 
contradiction  declares  that  we  cannot  conceive  of  a  t  ling  as 
being  and  not  being  at  the  same  time.  If  identity  declares 
that  A  is  A,  the  mind  refuses  its  assent  to  the  contradictory, 
A  is  not  A.  Upon  the  law  of  contradiction  is  based  all  neg- 
ative judgments  and  logical  distinctions. 

III.  Excluded  Middle.  This  law  asserts  that  there  can 
be  no  medium  between  the  dictum  of  identity  and  that  of 
contradiction,  or  it  excludes  such  a  medium.  The  two  propo- 
sitions, A  is  A  and  A  is  not  A,  being  of  such  contradictory 
nature  that  if  one  is  true  the  other  must  be  false  and  vice 
versa,  no  medium  between  them  can  be  conceived.  We  must 
think  of  either  the  one  or  the  other  as  existing,  and  they 
cannot  co-exist.  The  law  of  excluded  middle,  it  will  have 
been  seen,  has  been  set  forth  in  a  disjunctive  proposition, 
Either  A  is  A  or  A  is  not  A.  By  identity  and  contradiction 
we  conclude  that  if  one  contradictory  proposition  is  true  the 
other  is  false.  By  the  action  of  excluded  middle  we  reason 
from  the  falsehood  of  one  to  the  truth  of  the  other. 

IV.  Reason  and  Consequent.  The  principle  here  set 
forth  has  been  called  also  that  of  sufficient  reason.  This 
implies  that  wherever  a  reason  exists  there  must  exist  a  con- 
sequent, and  conversely,  wherever  we  have  a  consequent  there 
must  exist  a  sufficient  reason  for  it. 

Logic  applies  this  principle  directly  in  the  reasoning  pro- 
cess, and  forms  in  close  and  necessary  connection  the  series 
of  notions  which  thought  has  produced.  The  axiom  of  Rea- 
son and  Consequent  must  be  kept  quite  distinct  from  that  of 
Causality,  as  will  be  seen. 


THE    FUNDA.MKNTAJ.    LAW'S    OF    THOUGHT.  169 

It  is  a  significant  fact  that  these  laws  were  not  developed 
by  philosophers  in  the  order  stated.  The  principle  of  contra- 
dictio'ti  was  enounced  by  Plato  and  emphatically  stated  by 
Aristotle,  while  the  law  of  identity  was  not  enounced  as  a  co- 
ordinate principle  until  long  after.  Hence  there  has  been  a 
controversy  among  philosophers  which  of  these  is  the  first  or 
highf^st  principle ;  some  assert  that  our  own  existence  even  ia 
not  a  primary  datum  of  intelligence,  but  is  an  inference  from 
the  existence  of  thoughts  and  feelings  of  which  ^^ie  are  imme- 
diately conscious.  Some  would  claim  Identity  to  be  first  in 
order,  while  others  regard  Contradiction  as  the  principle  by 
which  Identity  is  established,  and  without  which  it  cannot  be. 
So  too  there  have  been  those  who  doubted  whether  contradic- 
tion was  really  a  primary  principle,  an  a  priori  datum  of  in- 
telligence, or  whether  it  was  not  a  generalization  from  our 
earliest  experience.  With  most,  the  essential  fad  is  identity, 
the  essential  law,  contradiction.  Leaving  such  matters  to  the 
metaphysician,  we  may  not  only  agree  to  consider  contradic- 
tion a  primary  principle,  but  go  farther,  and  assert  that  it  lies, 
as  it  were,  at  the  foundation  of  the  others,  and  is  implied  in 
them.     It  is  clear;  it  is  universal;  it  is  necessary. 

It  is  clear,  as  is  shown  by  the  fact  that  it  depends  on  the 
same  evidence  as  the  simple  notion  of  existence,  of  which  it 
is  an  afiSrmation,  in  that  whatever  w  cannot  not  be.  Thus  it 
establishes  identity. 

It  is  universal,  because,  as  the  idea  of  being  is  implied  in 
every  apprehension  and  in  every  principle,  so  is  this  distin(;t 
affirmation  of  it  applicable  to  all. 

It  is  necessary,  because  by  it  reason  must  be  guided  in  all 
ns  judgments,  since  through  the  excluded  medium  it  estab- 
lishes the  absolute  truth  that  being  and  not  being  cannot  sub- 
sist, together. 

Let  it  be  observed  that  we  do  not  say  that  the  other  prin- 
ciples may  be  demonstrated  by  the  principle  of  contradiction, 
but  it  holds  place  as  the  highest  principle  only  as  the  others 


170  LOGIC. 

may  be  resohed  into  it.  Demonstration  supposes  the  thing 
to  be  demonstrated  less  evident  than  the  medium  quo,  that  by 
which  it  is  demonstrated.  Now,  each  of  these  first  principles 
has  its  own  intrinsic  and  immediate  value  and  truth,  and  can- 
not be  demonstrated. 

It  further  appears  that  the  law  of  contradiction  governs  a  i 
the  principles  of  reason  as  a  motive  and  guiding  power,  in- 
fluencing the  intellect  to  give  its  assent  to  that  which  with- 
out it  would  be  incomplete  and  inert. 

In  necessary  truth,  the  intellect  affirms  the  truth  of  th 
principles  which  it  perceives,  because  it  sees  the  necessary  con- 
nection between  the  two  ideas  compared,  and  at  once  explains 
or  rather  satisfies  itself  of  the  necessity  by  the  principle  of 
contradiction ;  or  the  truth  of  this  principle,  as  an  intuitive, 
undemonstrable  truth,  is  sanctioned  by  the  truth  that  its 
contradictory  cannot  be. 

And  what  is  seen  in  necessary  truth  is  equally  manifest  in 
contingent  truth.  Truth  is  contingent  when  it  depends  for 
its  existence  upon  some  hypothesis  or  condition  or  cause  or 
fact.  Here  the  mind  discerns  that  the  truth  exists  because 
the  condition  exists  and  not  otherwise,  and  hence  by  the  law 
of  contradiction  that  its  contradictory  must,  on  the  same  con- 
dition, be  false. 

Without  entering  into  the  speculations  of  philosophers  in 
all  ages  of  history,  it  seems  to  us  that  the  principle  of  contra- 
diction is  the  foundation  and  ultimate  reason  of  all  proof 
and  of  all  assent  of  the  intellect;  that,  so  to  speak,  it  gives 
vitality  to  the  law  of  Identity,  and  suggests  the  necessity  of 
excluded  medium,  establishing  itself  as  a  sufficient  reason  for 
both. 

These  principles  are  intuitive  cognitions  or  a  priori  convic- 
tion, perceptions  from  which  we  reason ;  concerning  which  we 
cannot.  To  this  extent  they  are  incomprehensible ;  we  know 
them  to  be,  but  not  how  and  why  they  are.     They  are  called 


THE  FUNDAMENTAL  LAWS  OF  THOUGHT.    171 

a  priori  principles  because  they  are  before  nil  our  experience 
and  before  all  possibility  of  proof. 

Upon  them  are  based,  with  greater  or  less  claim  to  intui- 
tive judgments,  numerous  axioms,  such  as  the  whole  is  greater 
than  apart,  and  a  part  less  than  the  whole.  Two  things  which 
are  equal  to  the  same  thing  are  equal  to  each  other.  By  ex- 
tension of  these  axioms  in  Logic,  we  have  also  tiuo  terms 
which  agree  with  one  and  the  same  third,  agree  with  e^ich  other; 
and  of  two  terms,  if  one  agree  and  the  other  disagree  ivith  the 
same  third,  they  will  disagree  with  each  other. 

It  will  not  be  without  interest  to  say  a  few  words  in  this 
connection  concerning  the  question  of  causality,  or,  whence 
do  we  derive  our  notion  of  cause  and  effect?  Various  solu- 
tions have  been  proposed,  so  diverse  and  conflicting  as  to  be 
in  themselves  properly  named  series  implexa  causarum.  It 
seems  to  lie  so  near  the  first  efforts  of  the  mind  that  many 
philosophers  have  supposed  the  judgment  of  causality  to  be 
an  a  priori  knowledge  referable  to  a  special  principle  of  in- 
telligence designed  for  it,  and  it  alone.  Others  have  variously 
considered  it  to  result  from  experience,  induction,  general- 
ization and  custom. 

In  common  language,  the  phenomenon  may  be  thus  stated  : 
we  cannot  think  of  anything  beginning  to  be  without  think- 
ing of  its  having  already  existed  in  another  form — that  is,  the 
necessity  of  our  intelligence  makes  us  believe  of  anything 
that  it  has  a  cause ;  and  as  the  cause  by  the  same  process  is 
believed  to  have  a  cause,  the  mind  of  necessity  goes  back  in 
the  chain  of  causes  until  it  reaches  the  idea  of  a  first  cause. 
What  is  the  limit  of  the  mind  in  this  search  ?  This  limit  has 
been  called  The  Conditioned,  and  the  law  of  the  conditioned 
is,  that  all  that  is  conceivable— as,  for  example,  in  time  and 
space— is  bounded  or  limited  by  extremes  which  are  incon- 
ceivable and  contradictory,  one  of  which  must  therefore  be 
true.  Thus  we  have,  as  one  set  of  inconceivable  extremes, 
absolute   commencement    and    infinite    non-commencement. 


172  LOGIC. 

both  of  which  are  inconceivable,  and  yet  one  of  which  is  true 
The  conditioned  is  based  upon  the  principle  of  contradiction 
and  it  explains  the  true  theory  of  causality.     Thus  the  judg 
ment  of  causality  is  a  derived  judgment,  not  from  the  powei 
of  the  mind,  but  from  its  impotence  to  attain  to  the  extreme. 
When  an  object  appears  to  us  as  commencing  to  be,  we  can- 
not but  suppose  that  what  it  now  contains  has  existed  before 
in  some  form — that  every  thing  we  see  is  an  efiect  which  miist 
have  had  a  cause — but  why,  or,  of  what,  the  cause  is,  we  may 
be,  and  in  some  cases  must  be,  ignorant.     This  inability  of  the 
mind  to  reach  final  causes,  and  thus  to  complete  the  explica- 
tion of  the  principle,  is  expressed  in  negative  adjectives,  in- 
finite,  unendingy  illimitable. 


CHAPTER   XII. 

(54.)  Of  Certain  Modes  in  ^which  Logic  is  Appliea. 

It  is  not  within  the  scope  of  this  work  to  enter  upon  tht 
Aibject  of  applied  Logic :  this  would  require  an  investigation 
of  all  the  sciences,  or  at  least  of  a  very  numerous  classifica- 
tion ;  but  it  is  designed  to  explain  the  meanings  of  certain 
pi. rases  which  refer  to  the  general  applications  of  Logic. 

We  have  the  phrase  moral  reasoning,  ar^l  it  is  often  used 
as  if  conveying  an  opposite  or  contrary  meaning  to  demon- 
strative reasoning. 

This  has  reference,  not,  as  we  have  clearly  shown,  to  the 
kind  of  reasoning,  as  there  is  but  one,  but  to  the  nature  of 
the  evidence  employed,  the  meaning  of  evidence  being  thai 
'testimony  which  sets  forth  the  truth  of  a  proposition.  Then, 
noral  reasoning  is  the  use  of  evidence  in  moral  subjects,  and 
iemonstrative  reasoning  its  use  in  mathematical  subjects. 

Now,  evidence  may  be  of  three  kinds — that  is,  as  to  the  man- 
ner in  which  we  obtain  it ;  it  may  be  intuitive,  inductive  or 
deductive. 

Of  Intuition,  Induction  and  Deduction. 

We  come  now  to  consider  the  means  of  discovering  truth 
which  are  most  useful,  but  which  have  been  strangely  con- 
founded with  Logic.  They  are  processes  as  much  bound  by 
logical  laws  as  all  other  movements  of  the  reason  are. 

It  is  evident  that,  in  order  to  the  logical  process,  we  must 
have  premisses ;  now,  these  premisses  are  obtained  evidently 
by  the  three  methods  just  mentioned,  intuition,  deduction 
and  induction  or  experi"jent. 

15*  17.^ 


174  LOGIC. 

By  hUuition  we  mean  the  immediate  and  absolute  know 
ledge  which,  without  any  apparent  effort,  we  find  implanted 
in  us.  Such,  for  example,  is  the  aspiration  of  man's  soul 
after  a  Deity,  as  exemplified  in  the  religious  systems  of  all 
people,  even  the  most  barbarous,  and  such  as  the  existence  of 
certain  affections  and  notions  of  moral  conduct.  In  brief, 
consciousness  in  most  of  its  forms  and  the  testimony  of  our 
external  senses  are  said  to  be  sources  of  intuition.  The  truth 
of  axioms  is  dependent  upon  the  laws  of  identity  and  contra- 
diction. 

But  most  of  our  knowledge  is  derived  from  what  we  pos- 
sess already  in  another  form,  as  where  we  deduce  certain 
inferences  from  acknowledged  premisses  or  from  observation 
and  experiment,  and  generally  many  observations  or  experi- 
ments are  necessary  before  we  can  determine  a  general  law  * 
thus,  it  required  centuries  of  observation  to  determine  the 
Copernican  theory  of  our  solar  system ;  and  almost  all  the 
developments  in  natural  science  are  the  fruit  of  many  obser- 
vations and  experiments  aggregated  in  each  case  to  form  one 
general  law.  It  is  an  effort  of  man  by  a  close  study  of  the 
phenomena  (^<pavM)ii^va)  or  appearances  of  nature,  to  arrive  at 
some  degree  of  acquaintance  with  the  noumena  {vuoo/ieua)  or 
essences  of  its  objects. 

To  unite  these  was  the  aim  even  of  the  heathen  philoso- 
phers, and  with  their  obscure  lights  they  w^orked  ardently  in 
the  labor  ;  it  remained  for  a  doubter  (Sextus  Empiricus),  two 
centuries  after  the  coming  of  Christianity,  to  connect  them 
for  another  purpose,  and  that  was  to  arrive  at  a  suspension 
of  all  judgment  on  objects  whose  nature  is  obscure,  and  thus 
to  acquire  a  certain  repose  of  mind  (^arapa^ca)  and  perfect 
equanimity  of  disposition  (fierptoTraOeca).  But  the  inductions 
of  Sextus  were  never  really  performed ;  he  theorized  to  his 
skepticism,  and  his  theories  will  not  bear  the  rude  hand  of 
physical  practice. 

In  order  to  illustrate  the  difference  between  induction  and 


UF  CERTAIN  MODES  IN  WHICH   LOGIC  IS  APPLIED.       1  7A 

aeduction,  let  us  suppose  a  law  already  determined,  which  we 
Btate  in  the  proposition  A  is  B.  Let  any  number  of  particu- 
lar examples,  as  x,  y,  z,  range  under  this  law,  thus,  x  is  A, 
y  is  A,  z  is  A,  and  we  can  manifestly  reach  the  conclusion 
that  X,  y  and  z  are  all  and  severally  B. 

But  suppose  the  general  law  unknown,  and  that  it  be 
approximated  to  in  proportion  to  the  number  of  particular 
examples  ;  we  shall  thus  have  x  is  B,  y  is  B,  z  is  B,  etc.  ;  but 
X,  y,  z,  etc.,  as  we  increase  the  number  of  the  examples,  rep- 
resent the  class  A ;  hence  we  may  state  the  law  A  is  B,  the 
truth  of  which  will  depend  upon  the  number  and  extent  of 
the  experiments  performed  and  particular  instances  observed. 
Or,  to  recapitulate  in  syllogistic  form : 

Deduction.  Induction. 

{Law)    A  is  B.  {Part,  examples)  x,  y,  z,  etc,  are  B. 

{Part,  examples)  x,  y,  z,  etc.,  are  A.  A  is  the  class  to  which  x,  y,  z,  etc.,  belong. 

{Conclusion)  x,  y,  z,  etc.,  are  B.  (Law)  A  is  (likely  to  be)  B. 

Now,  there  are  certain  sciences  in  which,  from  the  nature 
of  things,  we  can  never  state  more  certain  results  from  induc- 
tion than  this  likelihood;  but  this  likelihood,  it  must  be 
observed,  becomes  greater  and  greater,  and  at  length  touches 
absolute  certainty,  when  we  examine  many  particular  in- 
stances and  find  none  of  them  failing  to  range  itself  under  the 
law  which  we  call  likely,  so  that  at  the  last  we  write  it  to  all 
intents  and  purposes  as  a  categorical  proposition,  A  is  E.  In 
some  sciences  we  may  exhaust  all  the  particular  examples 
and  finish  our  induction  by  a  certain  law ;  or  if  by  induction 
we  find  any  quality  or  property  to  belong  to  the  essence  of 
the  object  undergoing  the  experiment,  induction  in  both  cases 
has  led,  as  the  other  could  not,  to  certainty. 

There  are  two  kinds  of  induction,  material  and  fovTnal ;  and 
it  is  by  a  want  of  proper  distinction  between  them  that  the 
error  has  arisen  of  comparing  induction  improperly  with  the 
syllogism,  and  asserting  that  while  induction  is  one  kind  of 
reasoning  the  syllogism  is  another — i.  e.,  deduction. 

Hence,  Lord  Ba^on  and  his  followers,  finding  that  ded^idion 


176  LOGIC. 

generally  moved  from  what  was  contained  in  known  premisses 
to  lower  classes  or  individuals  contained  in  them,  threw  aside 
the  syllogism  as  useless,  and  inaugurated  induction  as  the 
new  Logic  of  experimental  philosophy.  A  simple  examina- 
tion of  material  and  formal  induction  will  set  us  right.  Ma- 
terial induction  is  the  process  of  experiment  and  observation — 
the  laborious  investigation  of  facts  as  to  their  discovery  and 
their  combination — but  formal  induction  is  obtained  by  the 
use  of  the  syllogism  itself,  not  confined,  as  some  writers  have 
attempted  to  show,  to  the  third  figure,  but  in  most  examples 
capable  of  being  at  once  written  out  in  the  first  figure,  the 
form  in  which  they  may  be  immediately  tested  by  the  dictum 
of  Aristotle,  as  in  the  example : 

Whatever  is  true  of  the  cow,  goat,  deer,  etc.,  is  Ukely  to 
Maj.  prem.  ^^  ^^^^  ^^  ^^^^  horned  animals ; 

Min.  prem.       Rumination  is  true  of  the  cow,  the  deer,  etc. ; 
Concl.  (Law).  Rumination  is  likely  to  be  true  of  all  horned  animals. 

The  naturalist  receives  this  as  the  only  just  conclusion  from 
the  formal  induction  to  which  the  syllogism  has  helped  him  ; 
but  having  as  yet  found  no  exception  to  the  rule,  he  writes  it 
out  boldly  and  without  fear  of  contradiction, 

All  horned  animals  are  ruminant. 

Of  certain  modes  of  using  Syllogisms. 

Argument  a  priori. — This  is  the  mode  of  passing  from 
known  antecedents  to  necessary  consequents,  or,  in  the  sci- 
ences, from  cause  to  effect.  Thus,  if  we  consider  the  being  of  a 
God  and  of  his  attributes  to  be  independently  known,  as  by 
intuition,  then  we  reason  a  priori  to  the  existence  of  his  works, 
the  universality  of  his  providence  and  the  gracious  designs 
of  his  redemption ;  this  reasoning  is  most  plainly  stated  in 
the  form  of  the  constructive  conditional  syllogism,  the  affir- 
mation of  the  antecedent,  or  cause,  helping  us  to  the  affirma- 
tion of  the  consequent,  or  effect. 

Argument  a  posteriori. — This  is   reasoning   from  effect  to 


OF  CEUTAIX  MODES  IN   WHICH    LOGIC  IS  APPLIED.        IT'^ 

came.  If,  l)y  an  inverse  process,  we  tirst  study  natural  re- 
ligion, and  experiment  upon  the  wonders  of  the  human  mind 
and  then  pass  back  from  these  works  around  us  to  the  estab- 
lishment of  the  existence  of  a  first  great  cause  who  must  have 
made  them  all,  we  are  said  to  reason  a  posteriori,  or  from  re- 
sults to  their  causes. 

Of  the  two  modes  of  reasoning,  both  are  useful  and  effect- 
ive, but  the  reasoning  d  priori  is  the  most  explicit,  stating  at 
once  the  cause  and  reason  of  the  effect  and  conclusion,  whilst 
that  a  posteriori,  though  equally  conclusive,  is  not  so  explicit, 
because  it  simply  proves  that  the  conclusion  must  be  true, 
although  not  stating  its  intrinsic  cause.  Thus,  we  prove  the 
existence  of  a  first  great  cause  from  his  works,  or  a  posteriori, 
since  he  is  self-existent  and  therefore  has  no  cause,  and  con- 
sequently his  existence  cannot  be  proven  a  priori. 

History  uses  both  forms,  and  combines  them  with  great 
success.  Taking,  for  example,  on  the  one  hand,  the  early  ele- 
ments of  a  nation's  life— its  people,  its  geography,  its  tenden- 
cies of  government — history  seeks  to  trace  these  to  their  legit- 
imate results  among  the  changing  scenes  of  national  ex- 
istence ;  while  on  the  other,  looking  around  at  the  present 
condition  and  conduct  of  a  nation,  she  takes  these  results,  and 
tracing  them  back,  in  careful  combination,  with  each  step  re- 
moved from  the  present,  she  seeks  for  their  early  and  prime 
causes  in  the  classic  times  of  the  country's  origin. 

Argument  a  fortiori. — This  is  a  method  by  which  we  estab- 
lish a  stronger  conclusion  even  than  ordinary  premisses  need 
to  warrant  us.     Thus  : 

A  is  greater  than  B. 
B  is  greater  than  C. 
A  is  greater  than  C. 

That  this  conclusion  is  just  there  can  be  no  doubt,  and  that 

the  form  of  it  is  not  exactly  that  of  the  regular  syllogism  i> 

equally  apparent. 

M 


1 78  LOGIC. 

To  apply  the  doctrine,  let  us  present  the  argument  by  t^eo 
metrical  notation,  and  we  shall  have — 


in  which  we  have  the  relative  greatness  of  A,  B  and  C. 

But  we  are  entitled,  it  is  evident,  to  put  this  in  the  syllo- 
gistic form : 

Bis  A, 

C  is  B, 

Therefore,  d  fortiori,  C  is  A, 

which  is  Barbara ;  or  ordinarily  Barbara  is  itself  the  argu- 
ment a  fortiori,  and  is  only  otherwise  when  A,  B  and  C,  in- 
stead of  being  unequal,  are  exactly  coincident. 

In  this  latter  case,  we  have  the  old  case  of  convertible  terms 
in  each  proposition,  which  is  not  set  forth  in  separate  form  by 
the  Aristotelian  Logic. 

This  reasoning  a  fortiori  is  very  effective  and  proper,  and 
was  used  by  our  Saviour  in  his  invectives  upon  Chorazin, 
Bethsaida  and  Capernaum  with  thrilling  effect.  So  also  is 
it  forcibly  used  by  the  apostle  to  the  Hebrews  (x.  28)  in  the 
words :  "  He  who  despised  Moses'  law,  died  without  mercy 
under  two  or  three  witnesses  :  of  how  much  sorer  punishment 
shall  he  be  thought  worthy,  who  hath  trodden  under  foot  the 
Son  of  God,"  etc. 

The  Investigation  and  Discovery  of  Truth 
We  shall  now  briefly  notice  the  forms  of  method  used  m 

investigating  and  discovering  truth,  to  which  at  every  step 

the  canons  of  Logic  may  be  applied. 

Man  has  an  inherent  desire  to  find  truth,  and  the  universe 

around  and  within,  the  realms  of  nature  and  the  domain  of 


THE  IXVESTIGATIOX  AND  DISCOVER V  OF  TRUTH.       179 

rniiid  call  that  desire  iuto  constant  activity.  This  curiosity, 
which  "  grows  by  what  it  feeds  on,"  leads  at  once  to  the  dis- 
covery of  trutli,  and  through  the  process  to  the  education 
and  development  of  his  faculties. 

The  methods  and  order  of  investigation  are:  1.  Jbserva* 
tion  ;  2.  Supposition  or  hypothesis ;  3.  Induction  ;  4.  The 
Dry  ;  5.  Fixed  law  or  fact. 

I.  Observation  is  applied  in  general  to  whatever  is  pre- 
sented by  the  senses;  by  it  man  discerns  at  once  objects  and 
facts.  It  includes  a  thoughtful,  attentive  outlook  upon  crea- 
tion and  a  determination  by  the  senses  of  the  marked  dis- 
tinctions between  existing  things,  and  leads  to  the  next  step 
in  the  order  of  inquiry. 

II.  Hypothesis  or  supposition.  Because  certain  things  or 
conditions  exist,  we  suppose  the  existence  of  causes  which 
produced  them,  or  of  certain  determinate  effects  which  spring 
from  them.  The  words  hypothesis  (Greek,  u-ortdrj^at)  and 
supposition  (Latin,  sub  and  pono)  have  the  same  meaning — 
an  underlying  basis  upon  which  to  build.  A  hypothesis 
assigns  a  probable  cause  or  a  reasonable  connection.  It  is 
indeed  a  gratuitous  assumption,  but  it  has  been  so  subjected 
to  metaphysical  conditions  that  it  may  be  correctly  and  prof*- 
itably  used  in  our  process  of  investigation.  A  just  hypothe- 
sis is  one  which  explains  many  phenomena  and  contradicts 
none,  and  it  is  a  necessary  condition  that  it  should  do  so 
when  no  other  hypothesis  can.  Thus  it  establishes  a  pre- 
sumption in  favor  of  our  law  or  conclusion  which  must  stand 
or  fall  by  the  next  step  in  the  process.  Induction.  Hypothe- 
sis is  often  incorrectly  confounded  with  theory. 

III.  Induction  is  systematic  experiment,  based  upon 
hypothesis.  Having  made  a  nidus  for  our  observations  and 
experiments,  we  test  it  by  phenomena ;  if  they  agree  with  or 
range  themselves  under  the  hypothesis,  we  approach  a  general 
law ;  or  if  not,  we  see  that  the  hypothesis  is  wrong,  and 
assume  a  new  one. 


( 80  LOGIC. 

IV.  Theory  is  the  probable  establishment  of  our  hypothe 
eis  through  the  medium  of  luduction.  In  proportion  as  oui 
experiments  conform  to  the  hypothesis  it  becomes  probably 
true ;  as  the  experiments  increase  in  number  and  still  con- 
form the  probability  approaches  certainty,  until  at  length 
we  either  reach  certainty  or,  satisfied  by  sufficient  induC' 
tion,  assume  it,  and  arrive  at  a  fixed  law  or  fact. 

It  will  be  obvious  that  these  forms  of  method,  although 
distinct,  really  run  into  each  other  more  or  less  as  we  pro- 
ceed ;  that  in  preliminary  observation  we  may  use  the  sim- 
pler modes  of  induction;  that  in  hypothesis  we  are  antici- 
pating theory,  and  hoping  that  we  have  probably  assumed  « 
law  which  shall  be  arrived  at.  But  in  systematic  investiga- 
tion they  are  mainly  used  in  this  order.  Thus,  Franklin 
observed  the  similarity  between  the  spark  from  an  electrical 
machine  and  a  flash  of  lightning ;  he  supposed  or  assumed 
as  a  hypothesis  that  they  were  the  same ;  he  experimented  by 
flying  his  kite  and  leading  the  lightning  along  its  string,  and 
he  then  stated  his  theory  of  electricity,  which,  covering  all 
phenomena  and  contradicting  none,  has  assumed  the  charac- 
ter of  an  established  law. 

Of  the  Nature  and  Kinds  of  Evidence, 

As  the  investigation  of  truth,  according  to  the  methods 
just  stated,  depends  on  evidence,  we  shall  merely  state  the 
nature  and  kinds  of  evidence  by  which  truth  is  established. 
Evidence  (e  and  video)  is  that  which  makes  a  fact  or  propo- 
sition clear  and  obvious  to  the  mental  vision. 

Consciousness,  the  hiowledge  of  the  existence  of  the  think- 
ing subject,  comprehends  all  its  phenomena ;  intuition  is  the 
act  of  the  mind  by  which  it  looks  at  and  into  itself;  through 
it  we  have  a  belief  in  our  own  existence,  faith  in  the  testi- 
mony of  our  senses,  a  reliance  upon  the  uniformity  of  Na- 
ture's laws. 

Sensation  is  the  effect  produced  upon  our  senses  by  contact 


KVIDKNCE.  181 

vv'ith  the  world  around  us.  Sensation  doe^  not  separate  the 
object  producing  it  from  ourselves.  Perception  is  the  im- 
pression made  by  an  object  upon  the  mind  through  sensation 
Through  perception  we  gain  the  idea  of  outness  or  external- 
ity, and  thus  detach  the  object  from  ourselves.  These  are 
the  conditions  necessary  to  evidence,  and  to  these  must  be 
Added  memory  in  its  most  extensive  meaning,  as  the  conserva- 
tive, the  reproductive  and  the  representative  faculty  of  the 
mind  through  which  these  conditions  are  made  available. 

Analogy  is  that  resemblance  between  circumstances,  rela- 
tions or  eifects  of  two  objects  by  which  the  mind  is  led  to 
accept  what  is  true  of  one  as  true  of  the  other ;  as  evidence 
it  is  by  no  means  sure,  but  often  corroborative,  where  other 
evidence  is  produced.  Induction,  or  systematic  experiment, 
is  valuable  as  evidence ;  in  the  words  of  Bacon,  "  Prudent 
questioning  is  half  the  science." 

And  last  we  have  the  Testimony  of  mankind,  which  is 
based  upon  our  natural  inclination  to  believe  in  the  expe- 
rience and  truth  of  others.  It  is  evident  that  Testimony 
will  depend  for  its  value  upon  the  capacity,  the  character, 
the  prejudices,  the  means  of  knowing  and  the  number  of  the 
witnesses. 

An  individual  of  average  mind  has  the  capacity  to  under- 
stand the  moral  and  physical  circumstances  by  which  he  is 
surrounded.  The  natural  desire  of  man  is  to  speak  the  truth, 
and  all  men  unite  in  despising  a  liar ;  and  while  on  a  given 
subject  one  man  may  have  only  partial  knowledge,  many 
who  are  cognizant  of  it,  by  bringing  each  his  own  partial 
knowledge,  will  present  fuller  and  more  trustworthy  testi- 
mony than  any  one  by  himself  Where  fact  is  in  question, 
the  truth  may  thus  be  readily  obtained  ;  for  the  chief  requisite 
is  honesty:  where  opinion  is  desired,  we  must  add  superior 
knowledge  and  aptvtude  which  will  give  authority. 
16 


CHAPTER    XIII. 

A  HISTORICAL  SKETCH  OF  LOGIC. 

(56.)  Division  of  the  Subject. 

Having  completed,  in  general  outline,  the  study  of  the 
Wmal  Logic,  in  its  present  condition  of  exactness  and  prac- 
tical use,  we  are  ready  to  go  back  to  its  feeble  beginnings, 
and  trace  it  in  its  slow  and  trammeled  movements  from  the 
days  of  the  early  Greek  Philosophy,  through  the  applications 
of  Roman  Science,  the  enlightening  process  of  Christianity, 
the  era  of  the  scholastic  subtleties,  the  dawn  and  advance  of 
Experimental  philosophy  and  the  metaphysics  of  the  eigh- 
teenth century,  down  to  the  controversies  of  our  own  day. 

Nor  are  we  yet  to  regard  the  science  of  Logic  as  estab- 
lished beyond  dispute,  and  fairly  stationed  among  its  sister 
sciences ;  it  is  yet  an  arena  of  dispute,  and  the  most  distin- 
guished philosophers  disagree,  as  has  been  seen,  even  as  to 
what  it  is  and  as  to  what  is  its  scope. 

It  would  be  of  great  interest  and  profit  to  take  such  a  his- 
torical view  in  detail,  but  the  limits  of  this  work  will  not 
permit  it,  and,  besides,  for  all  practical  purposes,  the  periods 
of  the  history  naturally  divide  themselves  into  four.  These 
so  much  transcend  all  others  in  interest  and  value,  and  so 
absorb  the  events  which  just  precede  or  immediately  follow 
them  respectively,  that  they  form  the  plainest  and  most  con- 
venient method  in  which  to  present  the  history  of  Logic. 
They  may  be  marked  by  the  titles — 

1.  Aristotle. 

2.  Christianity  and  Logic. 

3.  Bacon,  and  the  rise  of  Inductive  Science. 

4.  The  present  system. 

182 


DIVISION    OK    Tin:    SUBJECT. 


185 


1.  Under  the  first  may  be  classed  all  the  efforts  of  the 
human  mind  in  the  arrangement  of  a  canon  of  reasoning,  in 
that  early  time  when  knowledge,  preceding  method,  was  only 
seeking  in  darkness  and  obscurity  that  system  of  laws  and 
principles  by  which  alone  knowledge  may  be  made  available. 
Around  Aristotle,  too,  cluster  the  great  expansions  of  science 
which  were  due  to  the  conquests  of  Alexander  and  the  great 
kingdoms  of  his  successors. 

2  In  the  coming  of  Christianity,  Logic  found,  not  a  rival, 
but  a  guide,  and  in  the  early  Church  it  was  the  weapon  of 
their  spiritual  warfare.  To  the  Church,  as  the  representative 
of  Christianity,  is  due  much  of  the  good  of  scholasticism. 

3  Logic  was  the  servant,  the  ill-used  servant,  of  Inductive 
philosophy,  and  owes  much  of  its  long  bondage  and  oppres- 
sion to  the  illustrious  founder  of  the  system  of  Experimental 

philosophy. 

From  these  considerations  it  has  been  assumed  that  we  are 
better  able  to  look  into  this  history  now  that  we  are  acquainted 
with  the  scope  of  the  science;  otherwise,  we  might  fall  into 
the  same  ef  ror,  by  reason  of  the  honorable  company  m  which 
we  should  find  ourselves. 

4    Since  the  time  of  Lord  Bacon,  and  perhaps  by  reason 
of  his  example  in  condemning  the  syllogism.  Logic  has  been 
degraded  from  its  position  as  the  controller  of  the  reason  on 
all  subjects,  and  has  been  so  intermixed  with  Mental  phil- 
osophy as  quite  to  lose  its  identity  and  be  miscalled  by  ita 
own  name.     This  was  its  condition  during  the  eighteenth  cen- 
turv      In  the  nineteenth  there  have  sprung  up  many  cham- 
pions  of  Aristotle  and  the  syllogism,  among  whom  first  in 
distinction  is  Archbishop  Whately.     The  universal  principle 
of  reasoning  has  been  rescued  by  him  from  oblivion  and  deg- 
radation, and  Logical  science,  although  still  maligned  and 
fiercely  attacked,  seems  ready  to  take  its  permanent  place 
among  the  great  elementary  sciences  of  human  investigation 
Bnd  instruction. 


1 84  LOGIC. 

{56.)  Aristotle. 

It  must  be  considered  that  the  progress  of  such  a  science 
AS  Logic  was  necessarily  gradual  and  slow ;  that  from  the 
beginning  men  had  been  contemplating  the  operations  of  Ihe 
reason,  or  were  making  vain  but  progressive  efforts  to  dis' 
tinguish  the  exact  functions  of  the  reason,  among  the  tazy 
elements  of  the  human  intellect.  Many  men  had  collected 
much  material  which  lay  floating  in  a  chaotic  state  upon  the 
great  deep  of  the  human  mind. 

The  logical  doctrines  of  conception  as  expressed  in  termSy 
0^  judgments  as  formed  in  propositions,  were  known  to  Socrates 
and  Plato.  Indeed,  Zeno  the  Eleatic,  who  is  mentioned  as 
the  inventor  of  Dialectic,  had  invented  logical  puzzles  which 
required  an  investigation  of  the  laws  of  thought,  and  that 
caused  a  race  of  so-called  teachers  of  Dialectic  to  spring  up 
in  Greece. 

So  the  first  movements  in  Logic  were  trammeled  by  the 
ignorance  and  empiricism  of  those  who  called  themselves 
teachers. 

The  experience  of  our  own  age  has  taught  us  that  true 
science  is  more  impeded  and  injured  in  this  than  in  any  other 
way.  A  whole  class  of  speculative  logicians  in  the  early 
times  went  by  the  name  of  Sophists. 

We  are  accustomed  to  hear  the  Sophists  spoken  of  in  terms 
of  contempt,  and  sophistry  has  come  to  mean  Fallacy.  But 
we  should  err  greatly,  as  many  in  all  ages  have  erred,  if  we 
regarded  them  as  wholly  evil.  The  most  enlightened  writers 
of  modern  times  have  demonstrated  that  much  of  the  odium 
which  attaches  to  the  name  belongs  really  to  the  abuse  ol 
their  art ;  they  were  paid  teachers — among  w^hom  are  enu- 
merated Protagoras  and  Gorgias — whose  duty  was  to  train  up 
young  men  for  the  duties  and  pursuits  of  public  life.  The 
character  of  the  Greeks,  who  were  fond  of  riddles  and  dis- 
putes, and  the  errors  of  the  age,  led  to  their  real  sophistry, 
and  their  abuse  of  the  rhetorical  art  to  make  *'  the  worse  ap 


AlMSTOTI.E.  J8%l 

pear  the  better  reason;"  after  that,  their  efforts  were  not  tbi 
the  purpose  of  widening  the  range  of  knowledge  and  truth, 
but  really  served  to  check  these,  and  thus  give  a  free  course 
to  fallacious  reasoning. 

The  Logic  of  Euclid  consisted  in  negative  proofs ;  his  de- 
sign was,  in  encountering  an  opponent  in  controversy,  not  to 
attack  his  premisses,  but  his  conclusion. 

Chief  among  the  early  logicians,  as  he  is  distinguished 
among  the  sages  of  the  world,  was  Socrates. 

Much  interest  and  sympathy  attach  to  the  virtuous  and 
heroic  life  and  the  tragical  fate  of  this  wise  and  good  man ; 
but  it  is  principally  by  his  philosophy  and  logic  that  he  has 
been  useful  to  the  world.  Keeping  in  view  always  before  his 
numerous  scholars  the  dignity  of  Logic  as  a  science,  and  the 
loftiness  of  the  reasoning  powers,  he  guided  the  logical  pro- 
cesses by  what  is  now  called  "common  sense."  "This  is  im- 
plied in  Cicero's  declaration  that  Socrates  brought  philoso- 
phy from  heaven  to  earth.  Xenophon,  likewise,  tells  us  in 
his  '  Memorabilia'  that  when  he  wished  to  form  a  decision  on 
any  subject,  his  reasonings  always  proceeded  from  proposi- 
tions generally  assented  to  or  understood."  *  Condemning 
the  errors  into  which  the  Sophists  had  been  led,  he  claimed 
Truth  as  the  real  aim  of  reasoning,  and  established  in  all  his 
arguments  a  high  principle  of  moral  responsibility.  The 
analytic  process  was  that  mainly  employed  by  Socrates  ;  and 
thus,  when  Plato  appeared,  he  found  the  science  of  Logic 
and  the  art  of  Dialectics  presented  by  detached  and  isolated 
views  as  the  result  of  previous  investigations.  The  analysiJi 
had  only  prepared  for  the  synthesis. 

The  plan  adopted  by  Plato  was  the  Synthetic  method,  and 
by  this  he  worked  out  many  irreat  results. 

Perhaps  the  best  feature  in  the  Logic  of  Plato  was  that,  on 
approaching  the  science,  he  tells  us  to  keep  the  mind  free 
from  all  preoccupations  and  preconceptions :  he  declared,  as 
*  Bh'i  key's  Historical  Sketch  of  Loj^ic   t).  24. 


186  LOGIC. 

an  axiom,  that  "  Iguorauce  is  the  true  start-point  for  Science  ' 
Disputing  the  assertion  of  the  earlier  philosophers  that  sensa- 
tion was  the  foundation  of  truth,  he  proved  it  to  be  one  of  the 
instruments  by  which  truth  is  arrived  at.  Without  stopping 
to  give  a  sketch  of  his  system,  we  may  state  that  his  Logic 
and  theology  are  so  intimately  connected  that  we  may  judge 
of  the  vigor  of  the  one  by  ^he  developments  of  the  other.  He 
proved  the  existence  of  a  Deity  who  was  the  measure  of  all 
knowledge,  the  centre  of  all  truth ;  and  in  mysterious  lan- 
guage he  declares  that  this  centre  is  "  the  beginning,  middle 
and  end  of  all  things."  But  Plato  was  to  be  eclipsed  by  a 
greater  mind — in  fact,  one  of  the  greatest  minds  the  world 
has  ever  seen. 

When  much  material  was  thus  collected,  when  many  vague 
theories  had  thus  been  started,  and  when  crowds  of  ignorant 
pretenders  had  arisen  to  be  converted  or  silenced,  Aristotle 
came  to  create  a  new  system — to  enlighten,  to  harmonize  and 
to  sweep  away  all  the  errors  of  the  Dialecticians  and  the 
Sophists.  He  who  was  to  correct  the  characteristic  errors  of 
the  Greek  philosophy  was  himself  a  Greek.  The  Greek  mind 
was  eminently  a  curious  one.  All  the  speculations  of  philoso- 
phy, all  the  systems  of  Ethics,  were  directed  apparently  and 
nominally  indeed  to  the  discovery  of  truth ;  but  if  they 
reached,  by  specious  arguments,  a  pleasant  conclusion,  it 
mattered  little  for  pure  truth.  They  contented  themselves 
with  the  fruits  of  their  system,  once  that  system  was  estab- 
lished. 

The  Athenians  were  characterized  by  the  apostle  as  "  spend- 
ing their  time  in  nothing  else"  but  the  pursuit  of  novelty, 
and  they  were  but  the  types  and  representatives  of  the  other 
states  and  cities  of  Greece.  There  are  in  the  early  Greek 
authors  many  corroborations  of  the  apostle's  assertion. 

Aristotle,  building  upon  the  combined  foundations  of 
Socrates  aud  Plato,  discovered  many  new  principles  and 
established  new  rules,  until  he  had  elaborate*!  the  system  of 


ARISTOTLE.  18? 

Logic  which  we  have  at  this  day.  His  logical  works,  pub- 
lished in  full  under  the  title  of  "Aristotle  Organon,"  com- 
prise the  following  works:  1.  The  Book  of  the  Categories; 
2.  Of  Interpretation  ;  3.  The  Prior  Analytics ;  4.  The  Post 
Analytics ;  5.  Topics ;  6.  Of  Sophisms. 

Of  these  the  most  important  are  "  The  Book  of  the  Cate- 
gories" and  both  "Analytics."  We  shall  proceed  directly 
to  explain  their  meaning. 

He  drew  the  true  and  somewhat  nice  distinction  between 
Logic  and  Rhetoric,  and  established  the  fact  (a  fact  not  yet 
learned  by  many  who  call  themselves  logicians)  that  Logic 
is  not  concerned  with  the  truth  of  propositions,  but  only  with 
the  reasoning  upon  such  propositions  as  are  given  into  its 
charge.  If  the  premisses  be  true,  then  Logic  will  give  a  true 
conclusion,  but  if  the  premisses  be  false,  Logic  gives  a  false 
conclusion ;  but  in  this  latter  case  the  Logic  is  as  good,  the 
argument  as  valid,  as  in  the  former. 

In  establishing  his  dictum,  which  we  have  assumed  to  be 
the  universal  principle  of  reasoning,  he  laid  down  the  general 
law  of  Logic — a  law  which  has  been  misunderstood  and  mis- 
interpreted, for  this  dictum  was  not  a  model  of  common 
arguments,  but  simply  a  test  for  all. 

As  the  Greeks  looked  for  truth  and  found  that  Logic  did 
not  impart  it,  that  before  Logic  could  be  used  they  must  be 
possessed  of  premisses,  which  premisses  are  given  them  either 
by  intuition,  by  deduction  or  by  observation — i.  e.,  induction — 
they  either  abused  Logic  for  not  doing  what  it  could  not  pro- 
pose to  do,  or  else  injured  it  much  more  than  their  abuse 
crmld  do  by  using  it  as  a  vehicle  for  false  philosophy  and 
mythic  religion.  They  took,  to  save  themselves  the  trouble 
of  laborious  induction  in  search  of  premisses,  the  vagaries 
of  their  own  quick,  joyous  and  disputatious  minds,  and  thua 
prDduced  monstrous  and  absurd  conclusions  which,  since 
their  Logic  was  valid,  they  felt  satisfied  to  consider  as  true. 

The  union  of  this  Grecian  spirit  with  the  equally  vague 


188  LOGIC. 

and  fantastic  imagination  of  the  Orientals,  with  whom  hjf 
conquest  they  became  acquainted,  further  corrupted  thei' 
intellects,  and  robbed  Logic  of  its  true  character  and  mis- 
sion, leaving  the  whole  domain  of  Philosophy  without  the 
true  guide  of  Reasoning. 

Let  us  now  look  in  turn  at  the  logical  works  comprising 
Ihe  Organon. 

The  Categories. 

We  are  in  the  habit  of  using  the  word  category :  for  exam- 
ple, we  speak  of  a  person  or  thing  being  put  in  this  or  that 
category ;  the  word  and  its  use  we  owe  to  Aristotle.  His  cate- 
gories are  ten  in  number.  They  are  not  all  now  considered 
of  importance  in  classification,  but  are  still  worth  an  expla- 
nation as  the  original  system  from  which,  by  careful  elimi- 
nation, we  have  produced  our  own  later  classifications.  The 
categories  were  supposed  to  imply  answers  to  all  possible 
questions  concerning  a  term  expressing  an  act  of  apprehen- 
sion— i.  e.,  all  of  which  we  can  have  any  knowledge. 

1st,  Substance ;  2d,  Quantity  ;  3d,  Quality  ;  4th,  Relation  ; 
5th,  Action  ;  6th,  Passion  ;  7th,  The  Where ;  8th,  The  When  ; 
9th,  Position,  in  space ;  10th,  Possession. 

The  categories  may  be  thus  more  fully  explained : 

1.  Substance  may  be  defined  that  which  is  in  itself,  which 
may  be  conceived  as  existing  by  itself  This  is  divided  into 
spiritual  and  corporeal,  and  subdivided  according  to  classes, 
genera,  species,  etc. 

2.  Quantity  may  be  translated  how  much  or  hoiv  great, 
and  by  implication,  as  to  time,  how  long.  Thus,  under  the 
head  of  Quantity,  we  have  the  three  special  considerations 
of  Number,  Magnitude  and  Time  (as  to  duration).  Number, 
we  know,  is  either  abstract  or  concrete,  as  when  we  speak  of 
a  number  disconnected  with  any  objects,  or  of  a  number  of 
objects  and  things.  Thus,  quantity,  as  a  category,  covers  the 
science  of  arithmetic.     Magnitude  is  either  linear,  superfieiaJ 


ARISTOTLE.  189 

or  solid;  and  thus  its  genus  quantity  covers,  likewise,  the 
ecieuce  of  geometry.  Time  is  either  permanent  or  successive, 
and  is  used  to  indicate  the  movements  or  conjunctions  of 
Number  and  Magnitude. 

3.  Quality  describes  the  kind  or  sort  of  which  a  thing 
is,  and  is  subdivided  into  Habit,  or  a  quality  induced  by  fre- 
quent repetition  of  the  same  act,  as  virtue,  vice,  etc. ;  Inherent 
natt.re,  as  man's  reason.  From  these  grow  the  many  subdi- 
visions of  color,  sound,  hardness  and  shape. 

4.  Relation  is  the  consideration  of  two  or  more  objects 
with  reference  to  each  other.  The  first  object  of  two  is  called 
the  relative,  the  second  the  correlative,  as  prince  and  subject, 
master  and  servant. 

5.  Action  has  a  double  meaning ;  it  is  at  once  the  exer- 
tion of  power  by  one  body  on  another  and  the  effect  pro- 
duced by  such  an  exertion. 

6.  Passion  is  the  endurance  of  another's  action. 

7.  The  Where  includes  the  three  meanings  which  we 
express  by  the  words  where,  whence  and  whither,  as  iii  Phila- 
delphia, from  Neiv  York,  to  London. 

8.  The  When  has  reference  to  the  exact  period  of  time, 
and  not  its  duration,  which,  as  we  have  seen,  belongs  more 
properly  to  quantity.  The  When  may  be  expressed  by  the 
phrases  to-day,  to-morrow,  a  hundred  years  ago. 

9.  Position  has  reference,  not  to  the  place  where,  but  to  the 
posture  in  which,  a  body  is  found,  as  lying  down,  standing  up, 
kneeling,  etc.  The  question  then  is,  how  did  you  find  it?  not 
where  f 

10.  Possession  has  reference  to  something  belonging  to 
the  object,  or  placed  upon  and  clothing  it,  and  as  a  category 
covers  all  questions  concerning  the  rights  of  property. 

Of  these  categbries  it  will  appear  that  sid)stance  stands 
apart  from  the  rest  in  that  it  is  sensibly  existent  and  they 
are  all  af/r^^w^eo"  of  such  an  existence.  It  will  further  appear 
upon  examination,  that  Quantity  and  Quality  are  essential  at- 


190 


LOGIC. 


tributes,  i.  e.,  belong  to  the  essence  of  the  object  necessarily 
while  Relation,  Action,  Passion,  The  Wliere,  The  When,  Position 
and  Possession,  are  accidental   circumstances  which  may  be 
dissociated  from  it. 

To  render  this  clearer  for  facility  of  reference,  we  state  it 
in  a  tabular  form.  In  this  table  we  place  all  the  explanatory 
parts  as  by  the  rules  of  division  before  given,  but  number  the 
categories  that  the  eye  may  at  once  rest  upon  them. 

The  object  or  existence  expressed  by  a  term. 


Attributes  belonging 
to  the  substance. 


Circumstantial. 

I 
4,  Relation. 


1.  Substance. 


Habit. 


Essential. 


2.  Quantity, 


Number.  Magnitude. 


Inherent  nature. 


3.  Quality. 


Time. 


Shape,  etc. 


5.  Action.     6.  Passion.     7.  The  Where.      8.  The  When.      9.  Position.      10.  Possession. 

Aristotle  asserted  that  everything  which  could  be  said  of 
any  subject  is  included  in  one,  some  or  all  of  these  categories, 
and  his  own  illustration  of  their  use  is  one  of  the  simplest 
which  can  be  found.  It  was  as  follows:  " Substance,  7?ia?i ; 
Quantity,  one ;  Quality,  white ;  Relation,  greater ;  The  Where, 
in  the  Forum ;  The  When,  yesterday ;  Position,  sitting ;  Action, 
whatever  he  may  be  doing ;  Passion,  whatever  may  be  being  done 
to  him."" 

It  is  under  this  first  attempt  at  method  that  the  sciences 
began  to  range  themselves  in  classes,  and  by  this  all  other 
systems  of  classification  seem  to  have  been  suggested.  Thus, 
Substance  is  the  foundation  of  all  Physical  and  Historical  in- 
vestigation ,  Quantity,  the  subject  of  Mathematics ;  Quality, 
of  M'^dicine;  Relation,  of  Ethics;  Action  and  Quantity,  of 


ARISTOTLE.  191 

Astronomy,  Music  and  Mechanics ;  Passion  and  Action,  of 
Electricity  ;  the  Where,  of  Geography  ;  th(!  When,  of  Chro- 
nology ;  Position  and  Quality,  of  Sculpture  ;  Habit  and  Posi- 
tion, of  Fsiiuting  ;  and  so  each  art  and  science  would  be  found 
to  range  under  one  of  these  singly,  or  more  than  one  when 
combined. 

The  books  of  "Prior  and  Post  Analytics"  originate  and 
Tlevelop  his  system  of  the  doctrines  and  use  of  the  Syllogism. 
They  have  been  the  resort  of  all  writers  on  formal  Logic  since 
his  time,  and  there  has  been  but  little  alteration  in  his  method. 
Aristotle  established  but  three  figures  of  the  syllogism,  the 
fourth  being  afterward  added  by  Galen. 

In  his  book  of  Topics  he  discusses  the  subject  of  Predicables, 
or  Classes,  and  establishes  the  expression  of  a  predicable  to  be 
in  four  ways  ;  /.  e.,  by  genus,  differentia,  property  and  accident; 
in  these  he  implies  the  species,  since  we  have  seen  that  if  we 
add  the  diffei-entia  to  the  genus  we  obtain  the  species. 

In  his  book  of  Sophisms  he  states  thirteen  Fallacies  as  in- 
cluding all  those  which  can  bear  a  syllogistic  form.  Six  of 
these  refer  to  the  words  used,  and  are  called  Fallacies  in  die- 
tione,  and  seven  consist  in  the  mattei'  of  the  propositions,  and 
are  called  Fallacies  extra  dictionem. 

The  logical  works  of  Aristotle  seem  to  have  been  providen- 
tially preserved.  Transmitted  by  his  disciples  from  hand  to 
hand,  they  were  at  length  concealed  in  a  vault  during  one 
hundred  and  thirty  years,  until  they  had  mouldered  into  an 
almost  illegible  condition.  Restored  from  this  condition, 
they  came  by  the  fortmie  of  war  into  the  han  Is  of  a  Roman 
general,  and  tluis  were  given  a  second  time  to  the  world. 

We  cannot  pause  to  notice  all  the  changes  attempted  in 
Logic  and  Philosophy  from  this  time  until  the  Christian  era. 
xVfter  the  Peripatetics  came  Pyrrho  of  Elis  and  his  Skeptics, 
who  seem  to  have  employed  Logic  to  deny  the  possible  attain- 
ment of  pure  truth.  They  embodied  their  system  in  Ten 
Tropes,  or  logical  rules  for  the  government  of  mind  in  th»' 


1 92  LOGIC. 

search  of  truth.     Their  doubt  led  to  what  they  termed  a  sus 
pension  of  judgment  rather  than  a  positive  denial. 

Of  the  Epicureans  and  Stoics,  it  may  be  said  that  the} 
aimed  at  the  establishment  of  no  Logical  system,  but  rather 
a  few  tenets  in  the  shape  of  propositions ;  by  these,  as  doc- 
trines, they  guided  their  course. 

The  tenets  of  Epicurus  may  be  comprised  in  the  assertion^ 
that  "  whatever  is  useful,  pleasant  and  delightful   is  ^rue." 
This  is  to  assert  that  man's  senses  and  bodily  appetites  are 
the  only  test  of  truth.     These  have  been  called  his  "  emo- 
tional criteria." 

The  Stoics  rejected  the  categories  of  Aristotle  and  adopted 
four  of  their  own,  and  attained  the  conclusion  that  "  pain  is 
no  evil" — a  philosophic  stretch  of  the  imagination  which  has 
given  its  name  to  an  unshrinking  endurance  of  pain  and 
evil. 

Very  little  transpires  concerning  Roman  systems  of  Logic. 
Although  Cicero,  Maximus  of  Tyre  and  Galen  lay  claim  to 
the  title  of  logicians,  the  logical  system  of  Aristotle  was 
adopted  by  them  all ;  Rhetoric  became  the  more  valued  and 
important  study. 

The  history  of  Logic,  then,  from  the  time  of  Aristotle  to 
the  coming  of  Christ,  is  not  a  history  of  change,  but  the 
logic  of  Aristotle,  however  unchanged,  had  been  most  un- 
worthily used.  No  longer  the  guide  and  test  of  just  reason- 
ing, it  became  the  vehicle  of  ingenious  falsehood,  was  made 
to  support  any  theory  and  gave  power  to  its  possessor  "  to 
argue  on  both  sides  of  any  question."  To  satisfy  curiosity  it 
established  any  paradox,  and  one  being  made  the  premiss  to 
another,  the  error  was  multiplied  "  in  infinite  progression  un- 
defined." It  was  not  the  logical  system,  but  the  mind  of  man, 
which  needed  purification — not  abstract  propositions,  but  the 
matter  they  contained,  which  demanded  scrutiny. 

We  shall  see  also  that  the  misconception  of  the  sphere  of 
Logic  was  equally  fruitful  of  error  long  after  the  establish- 


THE    LOGIC   OF    CHRISTIANITY.  193 

ment  of  Christianity,  and  that  it  has  remained  for  the  iiiue- 
teentli  century,  not\vitlif?tanding  the  utmost  resistance  of  many 
learned  but  dogmatic  philosophers,  to  give  to  Aristotle  and 
his  system  their  true  place  in  the  domain  of  science — an  in- 
stauration  not  by  one  man,  a  new  Organon  not  the  product 
of  one  teeming  brain,  but  the  tribute  of  Philosophy,  induc- 
tive and  deductive,  to  Aristotle,  the  great  founder  and  framer 
of  that  system  which  alone  controls  the  unbridled  reason 
and  sends  pure  truth  into  the  channels  of  usefulness  and 
practice. 

But,  meanwhile,  the  coming  of  Christianity  was  to  produce 
great  marvels  in  the  domains  both  of  Logic  and  Philosophy. 

(57.)  The  Logic  of  Cliristianity. 

The  Logic  of  the  Grecian  schools  had  been  the  guide  of 
man's  Reason,  but  now  it  was  itself  to  be  brought  into  com- 
panionship with  a  higher  human  attribute,  Faith.  Premisses 
were  no  longer  to  be  sought  by  the  ordinary  means  of  evi- 
dence, but  to  be  supplied  in  a  new  and  marvelous  manner. 
Christianity  combined  this  new  element  with  Philosophy,  and 
taking  the  art  of  Logic  as  the  vehicle  of  its  great  truths, 
used  it  in  a  manner  at  once  beneficial  and  practical,  putting 
an  end,  as  it  seemed,  to  the  controversies  and  paradoxes  which 
had  beguiled  and  engaged  the  Greek  and  Roman  mind. 

By  this  new  tutelage  of  human  reason,  Christianity  pro- 
duced an  immediate  and  startling  change  in  Philosophy  by 
opening  the  Finite  upon  which  man  may  use  his  reason,  as 
well  as  indicating  the  Mysterious  and  Infinite  to  his  faith. 

As  much  as  we  may  despise  the  Greek  systems  of  specula- 
tive Ethics  upon  which  they  employed  their  nobler  Logic, 
we  must  remember  that  they  were  the  gropings  of  men  in  the 
dark,  pursuing  a  faint  glimmer  of  light  in  the  hope  that  it 
would  lead  them  into  the  full  sunshine  and  free  air  of  Truth. 
They  had  no  revelation  of  intelligible  fact  or  of  mystery. 
The  efforts  of  Plato  to  attain  to  different  degrees  of  know- 
17  N 


194  LOGIC. 

ledge  which  he  calls  "the  absolute,  the  probable,  the  imper 
feet,"  the  Politics  ai.d  Ethics  of  Aristotle,  the  bold  dicta  and 
quiet  endurance  of  the  Stoics,  the  "emotional  criteria  of 
Truth,"  propounded  by  Epicurus,  and  so  much  abused  by  his 
disciples,  were  all  vain  attempts  to  arrive  at  that  knowledge 
which  could  come  to  man  only  by  miraculous  revelation. 
God  vouchsafed  no  such  revelation  to  them  ;  it  is  no  cause  of 
wonder  that  they  erred  greatly  without  it. 

This,  then,  was  the  crowning  glory  of  Christianity,  that  it 
gave  to  man  pure  Truth,  and  furnished  him  with  a  world  of 
new  facts  upon  which  to  reason,  of  glorious  propositions  upon 
which  to  try  the  powers  of  his  Logic,  They  furnished  him  a 
boundless  field,  with  the  word  of  God  as  a  beacon  infallible, 
and  where  reason  could  not  obtain  internal  or  analytic  evi- 
dence, resting  its  judgment  on  external  evidence  as  a  basis. 
God  said  to  man.  Believe  and  ye  shall  be  saved. 

Unlike  the  Greeks,  the  Jews  had  always  possessed  this 
revelation  in  a  ceremonial  and  progressive  form.  Their  own 
Scriptures  had  disclosed  to  them  not  only  the  true  story  of 
man's  origin  and  fall,  but  of  God's  supremacy  and  his  gra- 
cious design  of  restoration,  and  their  prophets  had  told  them 
with  a  heavenly  Logic  of  Type  and  Symbol,  premiss  upon 
premiss  in  glorious  abundance,  of  that  certain  conclusion,  the 
advent  of  the  Messiah. 

The  "  fullness  of  time  "  came,  and  the  event  fulfilled  the 
prophecies,  the  conclusion  completed  the  premisses.  Chris- 
tianity brought  philosophic  as  well  as  religious  light. 

By  a  strange  infatuation,  they  who  had  thus  awaited  His 
coming  refused  Him  when  He  came ;  and  since  He  could 
not  be  the  glory  of  His  earthly  "people  Israel,"  He  was,  in 
a  truly  philosophic  sense,  "  a  light  to  lighten  the  Gentiles." 

In  three  centuries,  He  had  been  eagerly  embraced  by 
heathen  Rome,  and  the  Logic  of  Aristotle,  freed  from  its 
vile  and  improper  uses  and  used  as  the  propounder  of  a  full 
and  pure  creed,  was  applied  with  great  power  to  the  spread 


THE    J.OGIC   OF    CHRISTIANITY.  195 

of  the  Chritjtian  religion.  Where  fUl.<e  premisses  had  been 
ignorantly  used,  leading  to  a  false  conelusion,  or  where  false 
conclusions  had  been  improperly  deduced  from  true  premisses, 
everything  for  a  time  was  changed.  Truth  was  everywhere 
triumphant,  and  its  reign  seemed  to  be  eternal. 

Such  was  the  first  influence  of  Christianity  upon  Logic. 
Containing  in  itself  nothing  repugnant  to  reason,  it  gave  a 
host  of  new  and  glorious  truths  fresh  from  the  mouth  of  God ; 
it  simply  threw  away  the  vague  speculations,  the  unsound 
paradoxes,  which  had  been  heretofore  used  as  premisses,  and 
took  these  new  truths  to  reason  upon.  In  the  teachings  of 
our  Saviour  and  the  apostles,  it  need  scarcely  be  remarked, 
not  only  that  every  statement  is  true,  but  that  every  argu- 
ment is  valid. 

On  the  other  hand,  Logic,  turning  gladly  away  from  the 
subtleties  and  absurdities  of  mythical  philosophy,  pressed 
forward  with  ardor  in  the  task  of  systematizing  and  promul- 
gating the  new  doctrines  of  Christianity. 

In  this  manner  arose  the  logical  systems  of  the  early  Chris- 
tian writers  and  apologists  known  as  "  the  fathers."  There 
is,  indeed,  error  to  be  found  in  their  uninspired  writings,  such 
as  we  should  expect  in  all  human  productions,  but,  from  Jus- 
tin Martyr  to  St.  Augustine,  one  object  of  their  writings 
seems  to  have  been  the  harmonizing  of  Christian  doctrine 
with  the  Logic  of  Aristotle,  and  thus,  while  they  preached 
the  truth,  to  show  at  once  the  union  and  true  relation  of 
Reason  and  Faith.  How  well  they  succeeded  as  a  class  may 
be  seen  at  the  present  day  from  the  growing  interest  in  their 
writings  which  is  manifested  by  all  who  are  interested  in 
Religion  or  Philosophy.  Never  forgetting  that  they  were 
surrounded  by  enemies  and  error,  one  part  of  their  worka 
was  fiercely  controversial,  always  keeping  in  view  the  elen- 
chus,  and  warily  observing  an  opponent,  or  rather  the  many 
opponents  who  were  scrutinizing  their  deeds  and  words. 

Where,  in  the  old  system  of  Philosophy,  Sensation  was  the 


196  LOGIC. 

starting-point,  and  man  must  evolve  philosophy  from  within 
himself,  tliey  established  Revelation  as  the  centre  and  starting- 
point,  and  would  draw,  by  the  same  logical  formulae,  all  true 
philosophy  from  God.  From  this  time  Logic  Avas  insepara- 
bly connected  with  theology ;  the  Church  ruled  the  world. 

Tlie  Christian  Church  had,  in  its  union  with  the  Roman 
empire,  a  strength  and  stability  from  which  great  philosophic 
results  must  have  sprung ;  but  just  when  they  were  framing 
this  glorious  system  at  once  of  Religion  and  Philosophy,  the 
Roman  empire  of  the  West  fell  under  the  ruthless  attacks  of 
the  Northern  barbarians,  and  the  Church  was  temporarily 
paralyzed  by  the  shock.  For  centuries  after,  the  great 
efforts  of  the  Church  were  directed  to  the  attainment  of  a 
firm  social  basis  and  political  power. 

We  have  already  stated  the  connection  between  Logic  and 
Philosophy.  They  may  be  dissociated,  but  are  both  then 
useless.  Thus,  indirectly.  Philosophy  has  exerted  such  an 
influence  upon  the  uses  of  Logic  that  it  is  important  to  trace 
the  systems  with  which  Logic  was  combined,  and  to  promul- 
gate which  it  was  used  after  the  establishment  of  Christian- 
ity. Most  of  the  Christian  writers  investigated  the  subject 
of  the  human  reason,  and  studied  the  Logic  of  Aristotle. 

As  might  be  expected,  so  magical  a  transformer  as  Chris- 
tianity was  not  without  fierce  philosophic  opposition.  With 
equal  step  Skepticism  and  Heresy  advanced.  Those  who 
were  doubters  before  where  only  Science  was  concerned  were 
doubly  doubters  when  told  of  Christian  mysteries. 

The  representative  of  the  new  skeptics  was  Sextus  Empir- 
icus,  who  lived  in  the  beginning  of  the  third  century,  and 
who  was  but  a  new  incarnation  of  Pyrrho  of  Elis.  Unwill- 
ing to  receive,  on  prima  facie  evidence,  the  truth  of  the  new 
revelation,  they  had  fallen  back  upon  the  old  material,  and 
had  worked  to  the  same  results  as  the  Greek  philosophers ; 
they  turned  their  backs  on  the  light — which  admits  of  no 
better  proof  than  the  physical  light  of  day — and  walked  into 


THE    I.OGIC    OF    CHRISTIANITY.  197 

the  cave  of  darkness,  of  doubt  and,  iu  a  religious  view,  of 
despair. 

The  skepticism  of  Pyrrho,  three  hundred  years  before 
Christ,  was  consistent  and  well  deduced  when  compared  with 
this,  and  yet  Ihe  Greek  academicians,  we  know,  had  con- 
victed him  of  absurdity.  "  Because  everything  is  contra- 
dictory, everything  is  false."  Now,  if  this  be  true,  the  axiom 
itself  is  false,  and  so  the  skeptic,  thrown  upon  the  horns  of 
a  dilemma,  must  grope  again  in  vain  for  new  proofs  of  false- 
hood and  new  certainties  of  doubt. 

Of  the  Neo-Platonic,  Eclectic  or  Alexandrian  school,  the 
object  seems  to  have  been  to  unite  the  Greek  philosophy  and 
Oriental  dogmatism  into  one  system,  but  it  was  a  false  and 
feeble  combination,  fated  to  a  speedy  and  ridiculous  end. 

Its  metaphysics,  as  prepared  by  Plotinus,  was  the  attempt 
by  the  combination  of  heathen  obscurities  to  attain  to  Chris- 
tian light;  its  theology,  as  reduced  by  lamblichus,  was  a 
strange  retrogradation  from  the  Scriptures,  which  revealed 
the  person  and  word  of  God,  to  the  ridiculous  deities  of  the 
Pantheon ;  and  its  Logic,  of  which  the  great  Porphyry  was 
the  applier,  was  an  attempt,  by  the  use  of  the  Aristotelian 
system,  to  establish  all  these  errors,  at  the  expense  of  the 
fair  fame  and  even  of  the  existence  of  Logic. 

Nor  in  the  singular  application  of  Christianity  to  Logic 
must  the  Gnostics  be  forgotten.  Their  name  indicated  their 
creed ;  y^wtrc:;,  knowledge,  as  opposed  to  faith :  naked  Logic, 
stripped  of  its  armor,  was  made  again  to  do  duty  in  the 
ranks  of  the  Prince  of  Darkness.  Gnosticism  "  took  such 
portions  of  the  Gospel  as  suited  its  views  or  struck  its  fancy^ 
but  these  rays  of  light  they  mingled  with  such  a  chaos  of 
absurdity  that  the  apostles  would  hardly  have  recognized 
their  own  doctrines."  * 

The  greatest  perhaps  of  the  indirect  evidences  of  the  truth 
if  the  Christian  religion  is  that,  in  spite  of  the  false  systems 

*  Burton's  "Heresies  of  the  Apostolic  Age,"  p.  1  5,  quoted  bv  Neil. 
17* 


198  LOGIC. 

which  sprang  up  to  oppose  it,  it  has  steadily  and  mightilj/ 
prevailed ;  in  its  progress  it  has  purified  human  philosophy 
and  unfettered  Logic ;  but  it  did  not  accomplish  this  without 
fierce  contests ;  it  was  to  come  upon  dark  days  in  which  it 
was  the  only  glimmer  of  light — days  in  which  the  misuses 
of  Logic  were  no  longer  to  he  confined  to  profane  systems  jr 
heretical  creeds. 

Then  came  the  Schoolmen  or  the  so-called  Scholastics. 

The  first  era  of  Scholasticism  was  the  adoption  of  Logic 
as  the  form  and  vehicle  for  Religion,  and  thus  far  they  were 
in  the  right  path. 

The  second  phase  was  the  attempt  to  unite  Religion  and 
Philosophy,  and  this  produced  new  champions  of  Realism. 

The  third  phase  was  an  opposition ;  Religion  and  Philoso- 
phy were  rudely  dissevered,  and  this  produced  Nominalism. 

If,  now,  we  separately  consider  these  three  phases  of  the 
Scholastic  philosophy,  we  shall  perceive  that  the  first  was  the 
just  and  true  one,  and  that  the  succeeding  ones  were  learn- 
ing which  had  to  be  unlearned. 

That  part  of  the  Greek  system  which  could  be  made  the 
form  and  vehicle  of  religion,  as  it  is  of  all  correct  reasoning, 
was  only  the  Logic.  To  apply  that  to  the  service  of  Faith 
was  just  the  first  design  of  Christianity  toward  Logic,  and 
thus  far  the  Schoolmen  were  right — indeed,  it  would  seem 
ignorantly  right,  for  while  using  the  forms  which  constitute 
Logic,  they  still  persisted  in  calling  many  other  parts  of  the 
Greek  philosophy  by  the  name  of  Logic,  and  thus  making 
Logic  bear  the  blame  which  truly  belonged  to  the  errors, 
obscurities  and  absurdities  of  exploded  systems  of  metaphys- 
ics, theology  and  morals. 

This  is  apparent  in  the  works  of  Alcuin,  the  contemporary 
and  friend  of  Charlemagne,  and  especially  in  his  dialogues 
on  "  Grammar,  Rhetoric  and  Logic." 

Lofty  was  the  simple  distinction  of  St.  Anselm  that  there 
are  but  two  modes  of  Cognition,  Faith    and    Science,    and 


# 


THE   LOGIC    OF    Oil  KISTIANITY.  199 

grander   yet   the    idea,   "  that   Science    begins  where    Faith 
ends" — in  the  bosom  of  God! 

But  let  us  consider  the  second  and  third  phases. 

Nominalism  and  Realism  were  but  the  reproduction'  in 
the  ninth  century  of  the  old  Platonian  controversy  already 
referred  to.  Nominal  and  real  were  the  abstractions  of  what 
we  call  respectively  universal  and  particular. 

When  I  speak  of  a  single  man,  and  point  him  out,  I  desig- 
nate a  real,  existent  individual ;  when  I  speak  of  man  as  a 
common  term,  is  there  a  real  entity  corresponding  to  the 
word  ?  The  Realists  said.  Yes !  the  Nominalists  said.  No ! 
it  is  but  a  name  to  indicate  numbers.  This  had  been  the 
origin  of  the  controversy. 

Plato,  with  his  divine  but  vague  philosophy,  had  asserted 
that  there  was  a  real  existence,  an  archetype  in  the  bosom  ol 
iTod  corresponding  to  the  name  of  a  class,  as  man,  angel; 
Aristotle,  that  they  were  only  generalized  names  from  many 
individual  abstractions.  And  thus  these  great  parents  of 
Logical  Philosophy  set  the  example  of  wrangling  to  their 
myriad  children  of  the  schools.  It  is  curious  to  see  how 
such  a  dispute  first  connected  itself  with  religion.  It  was 
thus:  the  question  seemed  to  involve  another  and  a  more 
important  one,  viz. :  "  What  is  the  foundation  of  human 
knowledge?"  Roscellinus  of  Compeigne,  who  lived  in  the 
eleventh  century,  \vas  the  originator  of  the  new  controversy 
in  the  Middle  Ages  between  the  Realists  and  the  Nominal- 
ists. He  was  a  fierce  Nominalist;  and  as  this  led  to  supposed 
heresies,  he  was  an  object  of  persecution  on  this  account. 
As  warmly  was  the  cause  of  realism  espoused  by  William  of 
Champeaux,  and  throughout  the  schools  there  was  a  word 
war  of  great  fierceness  on  this  subject. 

Passing  over  the  quarrels  of  the  Schoolmen  until  we  reach 
the  time  of  Roger  Bacon,  and  thus  neglecting  many  great 
names  in  the  history  of  Logical  Philosophy,  we  are  struck 
with   the  power  of  his  experiments  and  analyses,  and  the 


200  LOGIC. 

manifest  fact  that  he  deserves  the  name  of  the  founder  of 
Experimental  Philosophy— that  his  "OpusMajus"  may  justly 
be  considered  the  precursor  of  ttie  "Novum  Organum''  of  hia 
more  illustrious  namesake,  Francis  Bacon. 

Disgusted  with  the  categories  of  Aristotle  as  trammeling 
an  ardent  physical  scholar  who  must  establish  categories  for 
himself  by  experience,  he  considers  experiment,  based  upon 
constant  observation,  the  only  rule  for  philosophy,  and  in  his 
works  in  the  laboratory  and  with  his  pen  we  discern  the  first 
dawning  of  the  day  of  Induction. 

For  a  while,  as  was  very  natural,  formal  Logic  fell  into  dis- 
repute, and  gave  way  to  experiment  in  physics ;  and  from 
that  day  down  to  our  own  times,  there  has  been  but  little 
appreciation  or  understanding  of  the  art  of  reasoning,  although 
it  has  been  constantly  used  and  constantly  ignored.  Like 
savages  who  breathe  the  invisible  air  round  them  and  are 
not  aware  of  its  existence,  so  minds  of  all  kinds  and  calibres 
have  used  the  Logic  which  they  found  established  as  the 
jirehicle  of  thought  without  knowing  where  to  make  their  ac- 
knowledgments. * 

(58.)  The  Logic  of  Experimental  Philosophy. 

Now  an  element  seems  to  have  been  introduced  into  phil- 
osophy which  till  then  had  been  considered  unimportant, 
and  that  was  observation  and  experiment;  or,  to  use  the  term 
by  which  we  have  expressed  the  methodical  and  successive 
observations  of  such  phenomena  in  nature  as  will  lead  us  to 
general  laws.  Induction.  Aristotle  himself  had  stated  the 
value  of  induction  for  the  discovery  of  new  truth,  and  men, 
in  all  ages,  had  used  it  as  an  exercise  of  common  sense  in  their 
ordinary  conduct ;  so  that  it  must  not  be  supposed  that,  in 
any  sense.  Bacon  is  its  inventor.  He  only  applied  it  by 
system  to  natural  science. 

IjOffic,  which  is  the  vehicle  of  truth  in  its  intellectual  pass- 
age  from  premiss  to  conclusion,  had  only  reasoned  upon  the 


THE    LUGIC    OF    EXrEKlMEJSTAL    i'llli.OSOriiY.       201 

known  and  conceded — mainly  from  some  general  law  to  a 
particular  example ;  now  its  premisses  were  to  be  new  truths 
aggregated  by  experiment ;  it  was  to  reason  from  many  par- 
ticular examples  to  the  establishment  of  a  general  law. 

Bacon  was  the  early  interpreter  of  Nature,  Descartes  more 
especially  the  analyzer  of  Thought.  To  each  is  due  an  illus- 
trious share  of  the  developments  in  philosophy.  But  Bacon 
is  the  more  distinguished  because  his  investigations  were 
made  in  every  domain  of  nature,  and  his  system  is  at  once 
more  intelligible  and  popular  on  that  account. 

The  starting-point  of  Bacon's  philosophy  was  the  assertion 
that  the  universe  is  a  great  storehouse  of  facts,  and  that  it  is 
man's  duty  and  interest,  and  it  ought  to  be  his  pleasure,  to 
explore,  discover  and  understand  these  facts,  not  only  in  their 
isolated  characters,  but  in  their  relations  to  each  other  and 
to  the  universe  itself.  His  experiments  and  his  use  of  the 
experiments  of  others  were  to  enable  him  to  arrive  at  general 
laws  of  the  universe.  Now,  corresponding  with  the  world 
around  us — that  is,  the  world  of  nature — there  is  a  world 
within  us,  the  world  of  Thought.  Let  either  be  impaired  or 
cease  to  exist,  and  in  just  such  a  proportion  is  the  other  im- 
paired or  does  it  cease  to  exist. 

To  unite  them  we  have  sensation  and  perception,  and  the 
union  is  lost  if  sensation  and  perception  fail. 

The  happy  union,  then,  of  Thought  and  Nature,  would  lead 
man  to  Truth,  and  to  attain  to  Truth  is  his  highest  aim.  It 
will  at  once  be  seen  that  this  was  the  establishment,  not  of  a 
logical,  but  of  a  philosophical  system.  But  to  proceed  :  the 
various  forms  which  truth  assumes  in  order  to  inspire  the  fac- 
ulties and  entice  the  pursuits  of  men  are  called  sciences,  and 
by  an  examination  of  multitudes  of  these  phenomenal  facta 
the  true  definitions  of  the  sciences  might  be  made,  their  true 
relation  determined  and  a  plan  of  classification  formed  for 
practical  purposes. 

Such,  then,  very  briefly,  was  the  aim  of  the  new  experi- 


202  LOGIC. 

mental  philosophy — a  great  restoration  which  was  proposed 
by  Bacon  in  his  Instauratio  Magna.  With  it  directly  Logic 
had  but  little  to  do,  but  that  little  led  men  of  science  into 
eirors  which  remain  to  the  present  day. 

Without  attempting  to  enter  into  the  details  of  the  "  Great 
Restoration,"  it  will  be  well  to  consider  some  of  the  steps 
proposed  by  Bacon  as  preliminary  to  it.  Finding,  in  his 
inquiries  about  facts  or  phenomena,  that  they  greatly  differ 
in  importance — that  some  are  simple,  others  complex,  some 
are  easy  of  interpretation,  others  very  difficult — he  proposed 
a  classification  of  the  instances  in  which  any  phenomenon  or 
fact  occurred,  and  this  should  be  a  sort  of  value  scale  of  the 
instances  in  which  a  special  phenomenon  occurred.  These  he 
calls  prerogative  instances,  or  those  cases  of  most  importance 
to  us  in  interpreting  a  fact  or  a  series  of  facts.  He  has 
stated  twenty-seven  of  these,  from  which  we  shall  choose  six 
as  better  illustrating  their  own  meaning  than  it  can  be  done 
m  other  w^ords.  Our  purpose  is  not  to  use  these,  but  merely 
to  indicate  their  nature  and  design, 

I.  Solitary  instances,  or  those  in  which  two  or  more  objects 
agree  or  differ  in  all  qualities  save  one.  Thus  a  rabbit-skin 
and  a  piece  of  rough  glass,  which  differ  in  all  other  qualities, 
agree  in  this,  that  on  being  excited  by  a  metal  they  both 
become  charged  with  positive  electricity,  while  two  pieces  of 
silk  ribbon,  only  differing  in  color,  when  thus  excited,  become 
the  one  positively  and  the  other  negatively  electrified. 

II  Forth-showing  instances.  Under  this  head  range  those 
facts  or  instruments  which  show  forth  the  quality  in  question 
in  the  highest  degree,  as  a  galvanic  battery  in  electricity  and 
a  barometer  in  pneumatics. 

III.  Analogous  instances.  Those  in  which  are  found  objects 
bearing  a  resemblance  of  purpose  or  relation,  however  unlike 
the  objects  themselves  may  be.  Thus,  a  camera-obscura  is 
analogous  to  the  eye  and  a  system  of  watermarks  to  the 
heart. 


THE    LOGIC    OF    EXPERIMENTAL    PHILOSOPHV.       203 

IV.  Crucial  instances.  There  are  two  probable  meanings 
to  the  word  crucial  as  here  used.  It  may  be  the  putting 
nature  to  the  torture,  the  crucifying  her,  to  wring  from  hei 
her  secrets,  or  it  may  have  reference  to  the  wayside  crosses 
which  at  the  parting  of  the  roads  indicate  the  true  direction 
to  the  traveler.  Franklin's  electric  kite  might  be  called  a 
crucial  instance,  in  the  first  sense.  Such  also,  in  the  second, 
was  Newton's  law  of  gravitation,  a  finger-board  for  ever  to 
point  to  the  true  direction  of  investigation  and  belief  con- 
cerning our  solar  system. 

V.  Varying  instances  (Instantice  migrantes).  Those  pro- 
pensities of  bodies  which  change  to  a  greater  or  less  degree. 
Among  these  would  be  included  change  of  form  from  solid 
to  liquid  and  from  liquid  to  gaseous,  and  the  reverse. 

VI.  Companion  and  hostile  instances.  Of  the  first  would 
be  qualities  which  usually  accompany  each  other,  as  heat 
and  flame ;  of  the  second,  those  which  are  never  in  conjunc- 
tion or  alliance,  but  seem  to  repel  each  other,  as  the  posi- 
tive and  negative  poles  in  electricity. 

The  other  instances,  which  we  cannot  stop  to  mention,  are 
designed  to  exhaust  the  classification  of  experiments  on  facts, 
and  to  lead  to  induction ;  and  here  began  the  danger  and  dif- 
ficulty ;  it  was  here,  also,  that  the  syllogism  which  Bacon 
despised  and  misunderstood  was  and  always  is  the  only  safe 
guide  of  Philosophy.  For,  suppose  the  facts  ranging  under 
these  instances  to  be  established,  how  many  of  them  will  give 
us  the  right  to  the  establishment  of  a  general  law  or  a  dis- 
tinct science  ?  We  have  seen  that,  in  most  sciences,  we  only 
attain  to  likelihood.  On  account  of  human  ignorance,  the 
process  has  been  this:  we  first  observ^e  a  few  facts;  we 
then  adopt  a  hypothesis  based  upon  them — i.  e.,  jump  at 
the  general  law — simply  in  order  to  make  a  nidus  for  our 
accumulating  facts,  and  thus  proceed  to  verify — if  the  new 
facts  will  verify — tnir  proposed  theory.  The  tendency  of 
man's  mind  is  so  great,  however,  to  repose  upon  a  darling 


204  LOGIC. 

hypothesis,  even  if  it  be  unsound,  and  rather  to  seek,  like  an 
advocate,  for  sucli  facts  and  statements  as  will  support  it, 
than  to  look  for  just  proof,  and  in  the  absence  of  such  to  dis- 
card it,  that  induction  has  often  led  to  grievous  error.  Many 
a  student  has  learned  on  hypothesis  some  part  of  Natural 
Science,  and  when  he  had  just  mastered  it  has  been  obliged 
to  discard  it  for  another. 

In  the  consideration  of  Judgment,  Bacon  has  given  special 
attention  to  the  fallacies  which  assail  the  mind  of  man. 
These  he  calls  idols  oj  the  intellect,  and  in  almost  every  case, 
since  they  are  contained  in  false  judgments,  they  belong  to 
the  class  of  material  fallacies.  But  all  these  idols  occasion- 
ally assume  the  garb  of  logical  fallacies. 

These  idols,  or  etdwXa,  which  Bacon  calls  "  the  deepest  fal- 
lacies of  the  human  mind,"  are  the  sources  of  error  which 
assail  men  in  their  investigations  in  Philosophy,  and  which 
"  must  be  renounced,  and  the  intellect  wholly  freed  and  puri- 
fied therefrom,"  before  we  can  hope  for  healthful  progress. 
By  the  word  idol  Bacon  means  the  prejudice  which  stands 
in  our  way  of  receiving  truth  and  the  bias  of  the  mind  from 
which  such  prejudices  arise. 

But  these  idola  will  most  clearly  explain  themselves ;  they 
are  of  four  classes — Idola  Tribus,  Idola  Specus,  Idola  Fori, 
Idola  Theatri;  and  with  reference  to  these  an  author  of  his 
own  time  remarks :  "  The  temple  which  he  purified  was  not 
that  of  nature  itself,  but  the  temple  of  the  Mind ;  in  its 
innermost  sanctuary  were  all  the  idols  which  he  overthrew." 

1  The  idols  of  the  tribe  are  those  which  are  imposed  upon 
the  understanding  by  the  general  nature  of  mankind ;  in 
other  words,  they  belong  to  the  human  tribe,  in  its  universal 
comprehension.  Thus,  he  asserts  that  men,  as  men,  are 
quicker  to  be  moved  by  affirmative  and  active  events  than  by 
negative  and  privative,  though  in  justice  they  should  be  moved 
by  both.  To  illustrate  this,  he  tells  the  story  of  the  Greek 
who  was  shown  in  Neptune's  temple  the  votive  pictures  of 


1.UGIC    OF    EXPERIMENTAL    PHILOSOPHY.  205 

those  who  had  escaped  shipwreck  ;  and  when  asked  if  he  did 
not  now  acknowledge  his  divinity,  said:  "Show  me  first 
where  those  are  painted  who  paid  their  vows  and  were  then 
ohipwrecked." 

2.  The  idols  of  the  den  or  cave  spring  from  the  nature  of 
each  particuhir  man,  and  grow  out  of  his  peculiar  features 
both  of  mind  and  body ;  these  may  also  be  fostered  or  devel- 
oped by  education,  custom  or  accident.  The  name  ia  sug- 
gested by  fancying  the  confusion  and  error  of  a  man  ]»eing 
brought  out  of  a  dark  den  or  cave  into  the  full  light  and 
glory  of  nature.  This  finds  its  counterpart  in  the  world  of 
philosophy,  where  men  only  emerge  from  the  den  of  their 
minds  to  find  confusion  and  disorder  in  the  beautiful  universe 
of  God. 

3.  The  idok  of  the  market  are  errors  which  grow  out  of 
words  and  cminnmication,  such  as  are  the  pass-words  and 
common  coin  of  conversation  and  intercourse  in  the  market- 
place ;  and  they  imply,  like  the  idols  of  the  tribe,  a  social 
organization,  but  on  a  much  more  limited  scale.  Instead  of 
being  universal  with  men,  they  are  errors  which  belong  to  a 
small  circle,  like  a  crowd  in  a  market-place,  moved,  at  the 
sound  of  an  orator's  words,  by  a  common  impulsion  of  pre- 
judice, passion  or  other  emotion.  These  idols  are  causes  of 
the  greatest  disturbance,  as  they  are  immediately  connected 
with  the  naming  of  things,  "  for  words  are  generally  given 
according  to  milgar  conception,  and  divide  things  by  such 
differences  as  the  common  people  are  capable  of;  but  when 
R  more  acute  understanding  or  a  more  careful  observation 
would  distinguish  things,  better  words  murmur  against  it." 

Thus,  many  words  in  our  every-day  use  convey  nc  definite 
meaning  to  the  mind,  but  have,  in  their  ver}'  indefiniteness,  so 
many  shades  of  meaning  that  they  are  a  constant  cause  of  ver« 
bal  fallacy.  As  special  reference  has  been  made  to  such  words 
in  the  chapter  on  Fallacies  (X.),  it  will  only  be  necessary 
to  mention  a  few  such  to  illustrate  the  idols  of  the  market- 
is 


206  LOGIC. 

place ;  such  is  the  word  republic,  which  we  have  been  apt  tc 
confound  with  democracy ;  Liberty  means  either  freedom  oi 
license,  as  its  champions  wish,  and  taste  and  beauty  have  as 
many  forms  as  there  are  eyes  to  see  or  imaginations  to  indulge. 

The  last  of  the  sources  of  error  enumerated  among  tht 
idols  of  Bacon  are  the  idols  of  the  theatre.  These  he  distin« 
guishes  from  the  others  as  perhaps  of  more  social  power  and 
influence.  Of  these  he  says,  "They  are  superinduced  by 
false  theories  or  philosophies,  and  the  perverted  laws  of  dem- 
onstration." They  are  comprehended  under  three  heads, 
Partisanship,  Fashion  and  Authority. 

Partisanship  is  the  generic  name  under  which  are  found 
factions  in  politics  and  in  religion,  and  under  whose  influence 
wars  of  creed  and  caste  have  so  often  desolated  the  world. 

Fashion  is  a  kind  of  partisanship  which,  however,  has  few 
opponents  and  no  great  rivalries,  but  which  pervades  society 
from  high  to  low.  We  do  not  refer  to  its  simple  sway  in 
dress,  equipage  and  social  life,  but  to  its  more  comprehensive 
dominion  over  all  the  works  and  thoughts  of  man,  over  art, 
science,  religion.  Great  masses  of  men  are  herded  like  cat- 
tle and  driven  willingly  in  the  train  of  this  all-swaying  Fash- 
ion, resting  their  happiness  here  and  their  hopes  in  an  eter- 
nal future  upon  the  dictum  of  Fashion. 

As  Fashion  partakes  of  the  nature  of  Partisanship,  so  is 
Authority  strengthened  by  an  alliance  with  both.  This  con- 
sists in  blind  obedience  to  an  existing  control  and  reliance 
upon  it  without  the  use  of  our  own  judgment. 

As  God,  who  has  given  man  Reason,  has  made  some  things 
higher  than  that  reason,  but  nothing  repugnant  to  it,  every 
theory  of  authority  in  Church,  in  State  or  in  general  philoso- 
phy is,  of  right,  to  be  examined  by  our  reason  before  we  can 
accord  to  it  our  belief.  Reliance  upon  authority,  without  a 
due  understanding  of  its  claims,  is  to  treat  our  own  moral 
constitution  with  injustice,  and  to  stop  the  wheels  of  healthful 
progress  both  of  individuals  and  societies. 


LOGir    OF    EXPERIMENTAL    PHILOSOPHY.  237 

In  reviewing  these  error-sources  it  is  scarcely  necessary  tc 
remark  that  it  is  the  abuse  and  not  the  use  of  our  words  and 
associations  which  lead  to  them. 

Thus,  the  idols  of  the  tribe  would  not  be  false  and  deceit- 
ful if  man  should  concur  universally  and  everywhere  in  just 
and  truthful  opinions,  nor  would  the  den  darken  men's  minds 
to  the  true  light  if  they  were  capable  of  carrying  into  their 
meditation  the  true  elements  of  combination  and  just  views 
of  the  objects  in  the  universe  around  them.  Heraclitus  has 
told  us  "  that  men  seek  the  sciences  in  their  own  narrow 
worlds  and  not  in  the  wide  one."  Such  is  the  influence,  but 
not  the  necessary  consequence,  of  the  den. 

So  it  is  easy  to  avoid  the  errors  which  grow  out  of  ambig- 
uous words,  such  as  those  which  mark  the  idols  of  the  market, 
by  demanding  just  definitions,  and  when  such  cannot  be  given 
either  agreeing /or  argument's  sake  upon  one  which  is  not  just, 
or  declining  to  argue  at  all  where  the  very  question  is  in- 
volved in  obscurity. 

We  may  observe,  concerning  the  idols  of  the  theatre,  that 
partisanship  has  its  good  as  well  as  its  evil  character,  and 
that  to  championize  the  right  is  noble  and  just ;  it  is,  how- 
ever, even  in  such  a  cause  that  its  tendency  is  to  extremes. 

So  fashion,  crowds  of  whose  votaries  are  miserable  and  self 
tortured,  is  incident  to  man's  social  character,  and  is  produc- 
tive to  those  who  use  it  aright  of  method  and  comfort  and 
success.  Although  fashion  has  done  much  evil,  it  could  not 
be  spared  in  our  social  or  intellectual  systems.  Nor  must 
Authority,  however  formidable  the  name,  be  accounted  of 
glight  importance,  for  under  just  authority  are  ranged  obe- 
dience, order  and  wholesome  discipline ;  without  it  government 
would  be  anarchy,  and  education  would  be  a  curse  instead  of 
a  blessing  It  is  the  time-honored  abu.se  of  it  which  de- 
mands our  dislike  and  resistance. 

Beyond  a  few  and  very  erroneous  allusions  to  the  Logic 


208  I.OGIC. 

of  Aristotle,  Bacon  and  his  immediate  successors  did  ver} 
little  for  it  as  a  science. 

Hobbes  seems  to  have  just  views  of  the  syllogism,  as  "  the 
instrument  of  demonstration,"  but  carried  his  investigations^ 
his  written  ones  at  least,  very  little  beyond  such  a  state 
ment. 

Resting  upon  the  basis  of  the  Baconian  philosophy,  the 
thinkers  of  the  seventeenth  and  eighteenth  centuries  seem  to 
have  neglected  the  art  of  reasoning  for  the  subject-matter  about 
which  we  reason,  and  thus  to  have  entirely  confounded  Logic 
with  the  art  of  thinking.  For  this  they  had  the  authority 
of  their  great  master,  Bacon,  who,  in  his  "  Advancement  of 
Learning,"  has  divided  the  Art  of  Judgment  into  Induction 
and  the  Syllogism ;  and  has  classified  as  four  kinds  of  demon 
stration  :  1.  That  by  immediate  consent  and  common  no 
tions ;  2.  By  Induction ;  3.  By  Syllogism ;  and  4.  By  Con 
gruity.  The  error  of  this  classification  is  at  once  apparent 
to  us. 

Indeed,  it  may  justly  be  said  that,  in  everything  pertaining 
to  Logic  in  its  proper  meaning.  Lord  Bacon  is  entirely  at 
fault,  while  in  everything  which  bears  upon  Experimental 
Philosophy  he  is  great  beyond  any  competitors,  for  he  is  its 
founder ;  and  as  a  few  words  have  shown  that  all  induction 
must  be  brought  to  the  syllogism  to  verify  and  test  the  laws 
at  which  we  arrive,  his  philosophy  can  be  easily  disconnected 
from  his  Logic,  and  the  faults  of  the  latter  exert  no  evil  in- 
fluence over  the  excellences  of  the  former. 

Many  logicians  in  England,  France  and  Germany  followed 
in  the  steps  of  Bacon  in  the  seventeenth  century,  attempting 
to  unite  Logic  and  Experimental  Philosophy  in  a  manner 
which  was  injurious  to  the  former. 

Locke,  misunderstanding  the  syllogism,  as  Lord  Bacon  had 
done,  discards  it  from  his  system,  and  bases  his  views  of  the 
understanding  on  two  sources  by  which  ideas  enter  the  mind. 
viz.,  Sensation  and  Reflection.     But  to  show  how  so  great  a 


LOGIC    IX    TIIK    LATEST    PERIOD.  20?> 

thinker  rebukes  himself,  he  states  reasoiiiug  to  consist  of  four 
parts:  1st.  Finding  proofs;  2d.  Arranging  them;  3d.  Show- 
ing their  connection  ;  and  4th.  Employing  them  correctly. 

Now,  what  is  all  this  but,  1st.  Finding  middle  terms  by 
ivhich  to  establish  premisses ;  2d.  Stating  syllogisms  ;  and 
ith.  Combining  arguments?  As  for  the  3d,  that  is  included 
in  the  2d,  for  they  cannot  be  arranged  without  their  connec- 
tion being  manifest. 

Leibnitz,  in  Germany,  seems  to  have  thrown  light  upon 
the  theories  of  Descartes,  and  to  have  elucidated  also  many 
things  in  Locke. 

Milton  has  been  called  the  most  learned  man  of  his  age ; 
he  vindicated  this  opinion  by  writing  upon  almost  every  sub- 
ject within  the  range  of  knowledge,  and  in  most  cases  writ- 
ing well.  We  are  not,  therefore,  astonished  to  find  that  he 
has  written  a  work  on  Logic.  It  is  in  Latin,  and  seems  to  be 
very  little  known.  In  that  he  adheres  to  much  of  the  Aris- 
totelian doctrine,  and  specially  championizes  Peter  Ramus, 
the  logical  Martyr.  He  divides  Logic,  which  he  calls  the 
chief  of  Arts,  into  two  kinds — Natural,  i.  e.,  the  faculty  of 
reason  in  the  human  mind ;  and  Artificial,  i.  e.,  rules  for 
directing  the  operations  of  that  faculty.  But  even  Milton 
erred  in  stating  that  "  it  belongs  to  Logic  to  lead  us  from  uni- 
versals  to  particulars,"  which  would  limit  the  Syllogism  to 
Deductive  reasoning. 

In  this  state  of  confusion  Logic  existed  until  the  new  rise 
of  Philosophy  in  the  eighteenth  century,  the  source  of  which 
was  the  continent  of  Europe  rather  than  England. 

(59.)  Logic  in  the  Eighteenth,  and  Nineteenth  Centuries. 

But  little  remains  to  be  said  in  order  to  complete  this  brief 
sketch  of  the  History  of  Logic.  Even  to  mention  the  names 
of  the  principal  writers  who  have  sprung  up  under  the  im- 
pulse of  the  Baconian  philosophy  from  that  time  to  the  pres- 
ent would  occupy  more  space  than  we  can  give,  and  to  dia- 
ls *  () 


210  LOGIC. 

cuss  their  metaphysical  works  would  in  this    connectiou   be 
difficult  and  improbable. 

The  logicians  of  the  eighteenth  century  seem  to  have  bent 
their  energies  to  the  task  of  classifying  the  science,  of  making 
such  a  logical  arrangement  as  would  make  much  labor  un- 
necessary and  find  for  each  its  true  niche  in  the  temple  of 
Truth. 

In  England,  Dr.  Isaac  Watts  published  a  treatise  on 
"  Logic,  or  Right  Use  of  the  Reason,"  which  is  a  compound 
of  Logic  and  Philosophy  alike  injurious  to  both.  Selecting 
a  few  tenets  from  Aristotle,  from  Lord  Bacon  and  from  the 
Schoolmen,  he  has  endeavored  to  harmonize  them.  In  an- 
other of  his  volumes,  "  The  Improvement  of  the  Mind,"  he 
has  moved  upon  surer  ground  and  with  much  better  success. 

Bishop  Berkeley  wrote  the  "  Principles  of  Human  Know- 
ledge"— a  work  of  profound  thought  and  excellent  reasoning  ; 
and  Bishop  Butler  has  exemplified  the  correct  use  and  appli- 
cation of  Logic  in  his  famous  treatise  on  the  ''Analogy  of 
Religion." 

France  has  also  produced  in  the  eighteenth  century  many 
fine  logical  minds  who  have  devoted  themselves  to  science 
specially  in  attempts  at  classification ;  among  these  were 
D'Alembert,  Diderot  and  their  coadjutors,  known  as  the 
Encyclopaedists,  w^ho,  in  the  eighteenth  century,  startled  the 
world  not  less  by  their  methodical  arrangement  of  the  sciences 
than  by  the  skepticism  which  their  studies  induced,  and  the 
atheism  or  denial  of  God's  existence  which  took  the  place 
of  doubt. 

It  would  be  impossible  in  a  treatise  of  this  kind  to  do  more 
than  simply  refer  to  the  present  writers  on  Logic  and  the 
present  condition  of  the  science. 

Archbishop  Whately  has  renewed  the  Logic  of  Aristotle 
in  its  pristine  vigor  and  placed  it  in  its  true  position  as  the 
only  sure  guide  or  Art  of  Reasoning.  Many  English  writer? 
have  difil'red  from  him,  some  in  his  conception  of  the  mean 


OF    CATEGORIES    AND    CLASSIFICATION.  21: 

iug  aiiil  scope  of  Logic  itself,  aiid  others  as  to  the  extent  tc 
whicli  the  Aristotelian  system  may  be  carried. 

Of  the  first  may  be  mentioned  Mr.  J.  8.  Mill,  whose  work, 
according:  to  the  view  we  have  taken,  mav  litlier  be  called 
"  an  encyclopaedia  of  philosophic  tenets  connected  with,  or 
resulting  from,  the  Science  of  Logic."  * 

Of  the  second  are  Sir  William  Hamilton  and  Mr.  Augus- 
tus de  Morgan,  who  would  develop  more  than  jour  categori- 
cal propositions  and  establish  what  we  have  called  the  "New 
Analytic,"  and  yet  they  differ  from  each  other  in  their  estab- 
lishment. Hamilton,  the  most  distinguished  philosopher  of 
his  age,  has  numerous  followers,  among  whom  are  Thomson, 
who  has  reproduced  the  Hamiltonian  Logic,  in  an  abridged 
form,  in  a  small  volume  called  the  Laws  of  Thought. 

The  most  important  changes,  however,  in  the  applications 
of  Logic  to  science,  are  to  be  found,  as  has  been  said,  in  the 
subject  of  Categories  and  Classification,  and  to  this,  in  illus- 
tration of  the  later  movements  of  the  science,  we  shall  now 
give  a  few  words.  It  will  be  at  once  perceived  that  the 
object  is  to  reach  a  summum  genus  under  which  all  the 
sciences  may  range,  and  then  by  a  logical  tree  of  division  to 
place  all  the  lower  classes  and  their  co-ordinate  species  in 
their  proper  places.  In  any  less  general  classification  it  is 
evident  that  the  principle  of  classification  will  be  changed 
for  the  different  sciences. 

(60.)  Of  Categories  and  Classification. 

This  is  a  part  of  the  duty  of  Method. 

The  Categories  of  Aristotle,  which  have  already  been  ex 

plained,  may  be  considered  the  basis  of  the  classification  of 

the  sciences ;  for  although  there  has  been,  in  former  times, 

much  dispute  concerning  their  true  reference — that  is,  whether 

it  be  to  words  or  things  or  conceptions — it  is  now  allowed  that, 

imperfect  as  they  are,  they  are  designed  to  apply  to  the  sinnma 

*  Neil's  Art  of  Reasoning^,  p.  234. 


212 


LOGIC. 


genera  under  which  all  things  which  are  named  may  range, 
themselves.  This  establishment  of  proper  summa  genera,  then, 
is  the  true  start-point  of  classification. 

Many  writers  have  simplified  these  categories  mainly  by 
reducing  the  number.  The  schools  of  Pythagoras,  Plato 
and  Epictetus  had  each  its  corresponding  list  or  table;  Locke 
wrote  three,  viz.:  Physica,  Practica  and  Semeiotiea,  or,  as 
they  have  been  translated.  Substance,  Modes  and  Relations ; 
Hume,  two,  viz. :  Ideas  and  Impressions. 

Among  German  philosophers  and  logicians,  Kant  holds  the 
highest  place.  His  views  are  principally  set  forth  in  his 
Critique  of  Pure  Reasori.  He  established  as  an  instrument 
for  a  pure  science  of  nature  the  following  categories,  logical 
and  transcendental : 

Logical.  Transcendental. 

C  Universal.  Unity. 

I.  Quantity.  <  Particular.  Plurality. 

(.  Singular.  Totality. 

r  Affirmation.  Eeality. 

II.  Quality.      <  Negative.  Negation. 

(.  Indefinite.  Limitation. 

r  Categorical.  Substance. 

III.  Relation.    <  Hypothetical.  Cause. 

(^  Disjunctive.  Reciprocity. 

r  Problematical.  Possibility. 

IV.  Modality.  -J  Assertory.  Necessity. 

(,  Apodictic.  Existence. 

Under  these  twelve  categories  all  forms  of  our  sensible 
experience  may  be  brought.  This  was  only  part  of  a  system 
of  philosophy,  including,  besides  Logic,  aesthetics  and  met- 
aphysics. 

But  these  are  manifestly  none  of  them  of  that  practical 
form  and  character  which  is  desirable  for  useful  reference, 
and  hence  it  has  been  the  aim  of  later  writers,  especially 
upon  Metaphysics  and  Logic,  to  write  out  tables  of  classifi- 
(nation  which  should  comprise  and   methodize  all  forms  of 


OF   CATEGORIES    AND    CLASSIFICATION  21 3 

human  scie/ice.  To  classify  palpable,  tangible  objects  is  to 
arrange  them  in  groups  according  to  a  certain  method,  and 
that  method  will  usually  be  based  first  upon  the  great  divis- 
ion of  kingdoms,  and  afterward  upon  the  relation  of  fpecies 
to  genus. 

If  we  reflect  for  a  moment  upon  the  innumerable  forms 
of  life  and  existence  in  the  three  great  kingdoms,  Animal, 
Vegetable  and  Mineral,  we  shall  at  once  be  struck  with  the 
difficulty  and  labor  of  a  just  and  adequate  classification  ;  and 
yet,  strange  as  it  may  seem,  true  progress  in  any  of  these 
branches  has  but  kept  pace  with  such  a  classification,  the 
naming  and  placing  of  a  minute  species  in  its  proper  place 
being  the  necessary  way  of  fixing  it  there  for  ever. 

It  has  already  been  said  that  the  basis  of  physical  classifi- 
cation is  the  establishment  of  the  summum  gemui,  and  that 
the  rules  of  logical  division  must  determine  all  the  subaltern 
genera  and  species.  This  must  serve  us  for  the  classification 
of  the  known  and  determined,  but  in  the  world  of  Theory 
another  mode  may  with  propriety  be  adopted :  it  is  the  classi- 
fication by  series,  investigated  by  Comte.  It  consists  in 
selecting  some  particular  phenomenon  the  laws  of  which  are 
to  be  investigated,  and  then  ranging  the  various  objects  which 
sustain  a  relation  to  it  in  a  nearness  proportional  to  thai 
relation. 

With  this  subject  of  classification  scientific  nomenclature  is 
immediately  connected,  and  it  will  appear  how  important  this 
must  be  regarded  when  we  consider  that  the  value  cf  the 
classification  will  depend  upon  the  names  of  the  difiereni 
classes,  as  to  their  j^recision  or  total  want  of  ambiguity,  theii 
completeness  or  expressing  the  whole  of  the  class  specified,  and 
their  expressiveness  in  denoting  the  properties  of  the  object  and 
the  reason  of  its  classifi^itiou.  Thus,  in  Chemistry,  a  law  of 
nomenclature  has  been  formed,  based,  indeed,  upon  sonu 
unfortunate  beginnings  which  have  been  allowed  to  remain 
but  very  systematic  and  universal  in  it;;  reception. 


214  LOGIC. 

But  the  high  aim  of  metaphysical  philosophers  to  smootL 
the  paths  of  Logic  has  been,  not  the  classification  of  one  sci- 
ence, but  the  analysis  and  classification  of  universal  Science, 
the  establishment  of  a  complete  table  in  which  all  human  in- 
v^estigation  should  find  its  place  and  link  itself  to  the  great 
aiind  of  all  ages  in  its  study  of  all  topics  within  its  sensual  ci 
intellectual  range. 

It  will  not  be  attempted  to  give  a  history  of  classification, 
Qor  to  prepare  or  copy  a  complete  table  of  any  previous 
author,  but  rather  to  indicate  the  manner  in  which  it  has 
been  done,  with  a  general  reflection  upon  the  results  attained. 
Classification,  to  be  logical  and  just,  must  be  made  after  cer- 
tain investigations  which  are  necessary  to  determine  the  true 
class  of  the  object  in  question.  This  will  be  done  in  Physics 
by  formal  analysis,  such  as  the  organic  analysis  in  Chemistry, 
and  in  the  exact  sciences  by  the  application  of  the  principles 
of  demonstrative  proof. 

Passing  by,  only  because  our  limits  do  not  permit  their 
consideration,  the  system  of  Bacon,  which  was  adopted  by 
the  French  encyclopaedists  of  the  last  century,  and  the  de- 
tails of  the  system  of  Locke,  we  come  down  to  our  own  times 
before  we  find  any  definite  attempt  to  supply  the  want.  An 
eminent  Scotch  writer,  as  he  reviewed  the  efforts  of  previous 
philosophers  to  classify  human  knowledge,  asserted  that  it 
was  an  impossible  task,  and  so,  from  its  magnitude,  it  would 
fairly  seem. 

Nothing  daunted  by  such  an  assertion,  Coleridge  suggested 
the  plan  of  classification  which  was  adopted  in  the  arrange- 
ment of  the  English  "  Encyclopaedia  Metropolitana,"  but 
which  he  found  to  require,  after  he  had  exhausted  his  cate 
gories,  an  additional  category  of  "  Miscellaneous"  species — 
the  unfortunate  subalterns  which  had  no  summum  genus 
under  which  to  range  themselves. 

Among  the  curious  but  highly  philosophic  remains  of 
Jeremy  Bentham  is  a  proposed  system  of  scientific  classifica- 


OF    CATEGOKIKS    AND    CLASSIFICATION.  ^15 

tioD ;  but,  like  his  other  works,  it  is  only  u  storehouse  of 
theory  from  which  less  gifted  but  more  practical  men  draw 
capital  for  constant  use. 

All  the  more  modern  writers  agree  in  considering  the  sys- 
tem of  Ampere  the  most  correct  and  useful.  It  is  based  upou 
the  two  categories  of  mind  and  matter,  and  under  these  it  ex- 
pands into  a  very  great  number  of  subordinate  sciences,  many 
of  which,  it  must  be  said,  are  created,  i.  e.,  in  name,  to  fill  up 
gaps  which  would  spoil  the  symmetry  of  his  table. 

It  is  not  our  purpose  to  write  out  his  table  in  full ;  it  would 
be  out  of  place  in  a  text-book,  as  it  could  only  be  examined, 
not  studied ;  but  we  will  form  a  tree  of  one  or  two  of  his  sub- 
jects to  illustrate  his  plan  and  indicate  its  truthfulness  and 
use. 

His  First  Table  contains : 

{Kingdoms.) 

/  Cosmological  sciences,  \  /    Noological  sciences,     \ 

\  i.  e.,  pertaining  to  matter.  /  \  i.  e.,  pertaining  to  mind.  ) 


Cosmologies  proper.  Physiologies.  Noologics  Social  sciences. 

I  I  proper. 


Mathematics.    Physics.    Mat.  sciences.  Med.  sciences.    Philosophies,  etc.    Ethnology. 

I  I  I  I  etc. 

Geometry,  etc.  etc.  etc.  etc.  | 

I  etc. 

Elementary  geometry,  etc. 

I 
Synthetical  and  analytical  geometry, 
etc. 

Of  these  there  are  several  tables  and  more  than  a  hundreil 
branches.  In  thus  indicating  rather  than  writing  out  in  full 
the  tables  of  Ampere,  we  spare  the  student  the  reading,  in 
place,  of  many  names  unknown  to  our  ordinary  .scientific 
studies,  such  iis  Dialegmatics,  Eleutherotcclmics,  Technesfhetic*, 
while  we  present  to  him  what  is  alone  our  present  purpose, 
the  theory  an  J  principle  of  classification. 


216  LOGIC. 

The  chief  merit  of  his  tables,  which  he  spent  his  life  m  con 
structing,  seems  to  be  that  there  are  no  cross  divisions — that 
no  subordinate  science  lies  out  of  its  own  class  or  laps  over 
into  another — errors  which  rendered  Bacon's  system  worthless, 
and  which  caused  Bentham  to  abandon  his  great  idea  and 
leave  it  in  its  inchoate  form. 

Auguste  Comte,  who  has  given  to  the  world,  in  his  Cours 
de  la  Fhilosophie  Positive,  his  views  of  philosophy,  did  not 
attempt  so  much  to  classify  science  as  to  determine  the  true 
relation  between  general  science  and  positive  science — to  make 
positive  science  more  general  in  its  application  and  general 
science  more  practical  and  positive.  This  has  been  his  life- 
work.  There  is  much  of  his  work  which  bears  indirectly  but 
dangerously  upon  religious  belief,  and  there  is  an  elaborate 
description  of  the  historical  progress  of  positive  science 
through  what  he  calls  the  mystical  and  metaphysical  eras  to 
the  positive. 

To  explain  more  clearly  his  view  of  this  positive  era,  it  is 
that  in  which  the  mysticism  or  mythology  of  ancient  and  early 
times,  as  well  as  the  crude  metaphysical  notions  of  the  Middle 
Ages  which  found  their  issue  in  astrology  and  magic,  are 
swept  away  by  the  light  of  modern  free  thought  and  investi- 
gation, and  in  their  place  are  substituted  the  laws  of  creation — 
laws  which  regulate  its  origin,  its  progress  and  its  destiny. 
There  are  six  positive  sciences  which  include  everything  that 
can  be  known.  These  are  Mathematics,  Astronomy,  Physics, 
Chemistry,  Biology  and  Sociology. 

But  it  is  not  within  our  scope  to  explain  his  philosophy ; 
re  have  only  to  do  with  its  Logic,  and  this  is  found  in  his 
cla?!sification. 

The  subject  of  classiticatiou  is  yet  open,  and  will  become, 
without  doubt,  clearer  and  more  practical  as  science  advances 
to  the  disco^^ery  of  the  proximate  laws  of  creation. 


CONCLUSION.  217 

(61.)  Conclusion. 

From  the  foregoing  investigation  of  the  art  of  Reasoning, 
we  may  pause  a  moment  at  the  end  to  reflect  upon  its  real 
value  and  importance.  If  Logic  is  really  the  art  which  con- 
trols and  guides  the  reason  in  its  workings,  and  without 
which  we  can  attain  to  no  truth  upon  which  the  reason  is 
exercised,  it  is  surely  worthy  of  a  high  place  in  the  catalogue 
of  elementary  studies,  and  the  statement  and  adoption  of  its 
laws  must  be  considered  of  the  first  importance. 

And,  above  all,  should  it  be  placed  upon  its  own  founda- 
tion, and  dissociated  from  any  other  sciences  which  either  rob 
it  of  its  own  identity  or  use  it  without  acknowledging  its 
jflSce. 

19 


APPENDIX. 

EXAMPLES  FOR   PRAXIS. 

IjOGICA^l  praxis  consists  in  the  application  of  the  rules  of 
Logic  as  a  test  of  all  the  forms  of  argument.  The  following 
examples  for  praxis  are  designed  to  give  ease  and  logical 
quickness  of  detection  to  the  student.  They  comprise  illus- 
trations of  all  kinds  and  forms  of  argument — regular  syllo- 
gisms, irregular  and  inverted  arguments,  compound  argu- 
ments, fallacies  of  every  kind,  curious  propositions,  examples 
of  the  processes  of  generalization  and  division,  amphibolous 
sentences,  etc.,  etc.  A  certain  number  of  these  should  be 
given  to  the  student,  as  an  exercise  with  each  lesson,  upon  the 
review  of  the  subject.  He  should  be  required  to  state  what 
each  is  in  its  present  form — if  2i fallacy,  of  what  kind;  if  a 
logical  fallacy,  to  write  it  out  by  symbols  and  thus  to  expose 
its  invalidity ;  if  an  inverted  argument,  to  put  it  in  the  true 
order  of  sequence  of  premiss  and  conclusion  ;  if  an  enthymeme, 
to  supply  the  suppressed  premiss  ;  if  in  an  imperfect  mood,  to 
reduce  it  to  one  of  the  perfect  moods  of  the  first  figure, — in  a 
word,  to  show  by  this  practice  the  truth  of  the  assertion  made 
at  the  beginning  of  this  book,  and  steadily  kept  in  view 
throughout  the  work,  that  every  valid  argument,  whatever 
its  form,  may  be  brought  directly  to  the  dictum  of  Aristotle 
as  the  final  test  of  argument. 

In  a  few  of  the  more  difficult  examples,  to  guide  the  student, 
a  reference  has  been  made  to  the  page  on  which  their  type 
may  be  found.  Some  selected  arguments  from  the  Latin 
authors,  generally  read  in  the  schools,  have  been  added,  as 
of  interest  to  the  classical  student. 

218 


EXAMPLES    FOU    PRAXIS.  21 S 

1.  Jupiter,  Saturn,  Venus,  Earth,  etc.  move  round  the  sun 
in  ellipses ;  these  are  all  planets ;  therefore  all  planets  move 
round  the  sun  in  ellipses. 

2.  Induction  is  the  only  true  science  of  reasoning ;  Syllo- 
gistic Logic  is  not  induction ;  therefore  Syllogistic  Logic  is 
not  a  true  science  of  reasoning. 

3.  No  one  is  good  who  commits  sin ;  all  men  commit  sin  ; 
therefore  there  is  none  good  except  God. 

4.  A  story  is  not  to  be  believed  the  reporters  of  which  give 
contradictory  accounts  of  it ;  the  story  of  Napoleon's  life  is 
of  this  kind  ;  therefore  it  is  not  to  be  believed. 

5.  Every  one  desires  happiness ;  virtue  is  happiness  ;  there- 
fore every  one  desires  virtue. 

6.  No  evil  should  be  allowed  that  good  may  result ;  all 
punishment  is  an  evil ;  therefore  no  punishment  should  be 

allowed. 

7.  Those  who  are  over-credulous  should  not  be  believed ; 
the  ancient  historians  were  over-credulous;  therefore  we 
should  believe  nothing  they  say. 

8.  An  American  citizen  should  be  free ;  I  am  an  American 
citizen;    therefore  I  should    be   allowed   to   do  whatever    I 

please. 

9.  The  duke  yet  lives  that  Henry  shall  depose,    (v.  p.  154.) 

10.  All  the  peaches  in  this  field  are  worth  one  hundred 
dollars  ;  this  is  one  of  the  peaches  in  this  field ;  therefore  it 
Is  worth  one  hundred  dollars. 

11.  Ought  we  to  act  from  expediency  as  a  motive? 

12.  Ought  not  children  to  obey  their  parents  ? 

13.  A  designing  character  is  not  worthy  of  trust ;  therefore 
I  do  not  trust  engravers. 

14.  All  good  men  are  beloved  by  their  associates  ;  this  man 
is  beloved  by  his ;  therefore  he  must  be  good. 

■^5  "^  Pallas  ne  exurere  classem 

Argivum  atque  ipsos.  potuit  submergere  ponti? 


* 


220  APPENDIX. 

Ast  ego  quae  Divum  incedo  regina  Jovisque 
Et  soroi  et  conjux,  una  cum  gente  tot  aunos 
Bella  gero. 

16.  Happiness  consists  in  obedience  to  the  Divine  Laws; 
this  obedience  is  virtuous  conduct ;  virtuous  conduct  is  the 
subordination  of  the  inferior  to  the  superior  in  our  nature ; 
4<Uis  subordination  is  induced  by  self-control ;  therefore  happi- 
ness is  the  result  of  self-control. 

17.  Crime  is  a  violation  of  the  laws  of  our  country;  piracy 
is  crime ;  this  man  belongs  to  a  band  of  lawless  men,  and 
this  band  has  been  taken  in  the  very  deed  of  piracy ;  there- 
fore he  has  violated  the  laws  of  his  country. 

18.  He  that  is  of  God  heareth  my  words ;  ye  therefore  hear 
them  not,  because  ye  are  not  of  God. 

19.  We  must  do  one  of  three  things — go  back,  stand  still, 
or  go  forward ;  we  cannot  go  back  or  stand  still ;  therefore 
we  must  go  forward. 

20.  "  Ay,  in  the  catalogue  ye  go  for  men — 

As  hounds  and  greyhounds,  mongrels,  spaniels,  curs, 
Shoughs,  water-rugs  and  demi-wolves  are  called 
All  by  the  name  of  Dogs." 

21.  All  that  glitters  is  not  gold ;  tinsel  glitters ;  therefore 
it  is  not  gold. 

22.  Warm  countries  alone  produce  wine ;  therefore  Spain 
produces  wine. 

23.  Quo  melior  servo  quo  liberior  sit  avarus. 
In  triviis  fixum,  cum  se  demittit  ob  asseni, 

Non  video.     Nam  qui  cupiet,  metuet  quoque  porro 
Qui  metuens  vivit,  liber  mihi  non  erit  unquam. 
Or,  The  fearful  man  is  not  free ;  the  miser  is  fearful ;  there- 
fore the  miser  is  not  free. — Hor.  Ep.  1,  16. 

The  following  strong  eulogiiim  of  Logic  is  an  argument  of 
the  schoolmen,  ivho  called  it  "  The  Divine  art ;  the  eye  of  the. 
hdellect ;  the  art  of  arts ;  the  science  of  sciences ;  the  bulwark 
o/  philosophy'  : 


EXAMPLES    FOR    PRAXIS.  221 

24.  Utque  supra  iKthereos  sol  aureus  emicat  ignes, 
Sic  artes  inter  proniinet  hsec  Logica  ; 

(^uid  ?     Logica  superat  solem  ;  sol  namque,  diurno 
Tem})ore  dat  lucera,  nocte  sed  hancce  negat ; 
At  LogiciL'  sidus  iiunquain  occidit ;  istud  in  ipsis 
Tani  tenebris  splendet,  quam  redeunte  die. 
Cum  hoc,  ergo  propter  hoc,  a  form  of  the   non   caiLna  pro 
caw^a,  is  broadly  illustrated  by  the  following : 

25.  The  encroachment  of  the  sea  upon  that  bank  upon  the 
coast  of  Kent  known  as  the  Goodwin  Sands,  rendering  it  very 
dangerous  to  navigation,  led  to  the  appointment  of  a  com- 
mittee of  parliament  to  inquire  into  the  subject.  The  com- 
mittee went  down,  and  examined,  among  other  witnesses,  an 
old  man,  who,  when  asked  what  he  regarded  as  the  cause  of 
this  encroachment,  replied,  after  some  minutes'  thought,  that 
he  did  not  know,  unless  it  had  something  to  do  with  Tenter- 
den  steeple,  a^  he  remembered  nothing  of  the  kind  before 
they  began  to  build  that  steeple,  but  it  had  been  steadily 
growing  worse  ever  since. 

26.  Horses  are  stronger  than  men ;  elephants  are  stronger 
than  horses ;  therefore  elephants  are  stronger  than  men. 

27.  Men  need  the  restraints  of  government,  because  they 
have  vicious  propensities. 

28.  Unjust  laws  endanger  the  stability  of  government,  be- 
cause ( ) ;  laws  which  enslave  man's  conscience  are  un- 
just because  , ) ;  therefore  laws  which  restrain  tlie  f^et^ 

dom  of  conscience  endanger  the  stability  of  government. 

29.  If  we  suppose  the  telegraphic  connection  from  London 
to  be  made  around  the  world,  and  the  transmission  to  be 
instantaneous,  then  a  message  starting  from  London  at  12 
o'clock  to-day  would  reach  London  at  12  o'clock  yesterday. 

30.  If  men  are  to  be  punished  hereafter,  God  must  be  tlie 
punisher;  if  God  be  the  punisher,  the  punishment  must  be 
just;  if  the  punishment  is  just,  the  punished  must  be  guilty  ; 
if  they  are  guilty,  they  could   liave  acted  otherwise  ;  if  thej 

19  » 


222  APPENDIX. 

could  have  acted  otherwise,  they  were  tree  agents ;  therefore 
if  men  are  liable  to  punishment  in  another  world,  they  must 
be  free  agents. 

31.  This  medicine  cured  a  very  difficult  case  of  disease  , 
therefore  it  will  cure  every  disease. 

32.  Among  the  most  bitter  persecutions  known  to  hislorj 
were  those  of  the  French  Revolution ;  therefore  they  must 
have  been  religious  persecutions. 

33.  Testimony  is  likely  to  be  false ;  the  existence  of  the 
Pyramids  depends  on  testimony  ;  therefore  we  may  doubt 
whether  there  are  pyramids  in  Egypt. 

34.  No  man  can  perform  impossibilities ;  a  miracle  is  an 
impossibility ;  therefore  no  man  can  perform  a  miracle. 

35.  With  God  all  things  are  possible. 

36.  No  man  can  do  these  miracles  which  thou  doest,  ex- 
cept God  be  with  him. 

37.  Si  testibus  credendum  sit  contra  argumenta,  sufficit, 
tantum  judicem  esse  non  surdum. — Bacon's  Antitheta. 

38.  Hsec,  si  displicui,  fuerint  solatia  nobis  ; 

Hsec  fuerint  nobis  prsemia,  si  placui. — Martial. 

39.  From  the  existence  of  bad  morals  springs  the  making 
of  good  laws ;  from  good  laws  arises  the  safety  of  the  com- 
monwealth ;  from  the  safety  of  the  commonwealth  all  social 
good  things  flow ;  therefore  from  the  existence  of  bad  morale 
come  all  good  things  to  society. 

40.  Si  saperem  odissem  jure  sorores, 
Numina  cultori  perniciosa  suo. 

At  nunc  (tanta  meo  comes  est  insania  morbo), 
Saxa  memor  refero  rursas  ad  icta  pedem. —  Ovid. 

41.  Csesar  oppressit  patriam ;  Tullius  non  oppressit  patriam ; 

ergo  ( ). 

42.  Una  Eurusque ;   notusque  ruunt,  creberque  procellis, 

Africus. 

43.  For  whom  he  did  foreknow,  he  did  also  predestinate 


EXAMPLES    FOR    PRAXIS.  223 

to  be  conformed  to  the  image  of  his  Sou  ;  that  he  might  be 
tlie  first  born  iimong  many  brethren.  Moreover,  whom  he 
did  predestinate  them  he  also  called;  and  whom  he  called 
them  he  also  justified;  and  whom  he  justified  them  he  also 
glorified.   Rom.  viii.  29,  30. 

44.  When  the  sun  is  in  Cancer,  it  is  summer ;  it  is  now 
summer  ;  therefore  ( ). 

45.  All  persecution  for  conscience'  sake  is  unpleasing  to 
God,  because  it  is  injustice. 

46.  Genius  must  join  with  study  to  make  a  great  man; 
this  man  will  never  be  great,  for,  though  he  has  genius,  he 
cannot  study. 

47.  No  man  can  serve  two  masters. Ye  cannot  serve 

God  and  mammon. 

48.  Pride  and  innocence  are  incompatible.  The  angels 
are  innocent ;  therefore  ( ). 

49.  In  this  life  we  must  either  obey  our  vicious  inclinations 
or  resist  them  ;  if  we  obey  them,  we  shall  have  sin  and  sorrow ; 
if  we  resist  them,  we  shall  have  pain  and  labor ;  therefore  we 
cannot  be  free  from  trouble  in  this  life. 

50.  This  doctrine  cannot  be  proved  from  the  Gospels ;  nor 
from  the  Acts  of  the  Apostles  ;  nor  from  Epistles ;  nor  from 
the  Revelation  of  St.  John  ;  therefore  it  cannot  be  proved 
from  the  New  Testament,     (v.  p.  175.) 

51.  It  is  a  sin  to  kill  a  man  ;  a  murderer  is  a  man  ;  there^ 
fore  he  should  not  be  hanged. 


These  examples  may  be  increased  at  the  pleasure  of  the 
teacher.  The  author  would  suggest  that  it  would  be  well  for 
students,  in  their  readings  both  of  verse  and  prose,  and  in 
their  classical  studies  as  well  as  in  English,  to  cultivate  a 
habit  of  marking  the  different  logical  forms  of  discourse.  It 
would  soon  become  a  pleasant  pastime,  as  well  as  a  profitable 
lesson.  .    '         „, 

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